text stringlengths 1 2.12k | source dict |
|---|---|
The following vector q is a 3 × 1 column vector containing numbers: $q=\begin{bmatrix} 2\\ 5\\ 8\end{bmatrix}$ A row vector is an 1 × c matrix, that is, a matrix with only one row. A column vector is an r × 1 matrix, that is, a matrix with only one column. 2. Column and row vectors a matrix with one column, i.e., size n×1, is called a (column) vector a matrix with one row, i.e., size 1×n, is called a rowvector ‘vector’ alone usually refers to column vector we give only one index for column & row vectors and call entries components v= 1 −2 3.3 0.3 w= −2.1 −3 0 4. Two matrices of the same order whose corresponding entries are equal are considered equal. A column matrix is a matrix that has only one column. Rectangular Matrix A matrix of order m x n, such that m ≠ n, is called rectangular matrix. To understand what this number means, take each column of the matrix and draw it as a vector. One column matrix. A matrix with only one row is called a.....matrix, and a matrix with only one column is called a.....matrix. Suppose that A has more columns than rows. The matrix derived from a system of linear equations is called the..... matrix of the system. The entries are sometimes A matrix is said to be a column matrix if it has only one column. 5. A matrix with only one row is called a _____ matrix, and a matrix with only one column is called a _____ matrix. The entries of a vector are denoted with just one subscript (since the other is 1), as in a3. A matrix with only one column, i.e., with size n × 1, is called a column vector or just a vector. 3. Column Matrix A matrix having only one column and any number of rows is called column matrix. 3) Square Matrix. For example, four vectors in R 3 are automatically linearly dependent. In general, B = [b ij] m × 1 is a column matrix of order m × 1. one column (called a column vector). Converting Systems of Linear Equations to Matrices. A matrix having only one row is called a row matrix (or a row vector) and a matrix having only | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
A matrix having only one row is called a row matrix (or a row vector) and a matrix having only one column is called a column matrix (or a column vector). INCLUDES THE SOLUTIONS. Sometimes the size is specified by calling it an n-vector. A column matrix has only one column but any number of rows. Below, a is a column vector while b is a row vector. Each equation in the system becomes a row. For example, $$A =\begin{bmatrix} 0\\ √3\\-1 \\1/2 \end{bmatrix}$$ is a column matrix of order 4 × 1. The variables are dropped and the coefficients are placed into a matrix. Each variable in the system becomes a column. Determinants. I want the corresponding rows of column one to be printed as follows : a = 3 2 1 3 2 5 4 8 5 9 I tried sort(a), but it is sorting only the second column of matrix a. row column. Fill in the blanks. A matrix with only one row or one column is called a vector. a = 7 2 3 , b = (− 2 7 4) A scalar is a matrix with only one row and one column. I have the matrix as follows. Example: D is a column matrix of order 2 × 1 A zero matrix or a null matrix is a matrix that has all its elements zero. augmented. The determinant takes a square matrix and calculates a simple number, a scalar. A wide matrix (a matrix with more columns than rows) has linearly dependent columns. Example: C is a column matrix of order 1 × 1 A column matrix of order 2 ×1 is also called a vector matrix. Then A cannot have a pivot in every column (it has at most one pivot per row), so its columns are automatically linearly dependent. a = 1 3 2 5 3 2 4 8 5 9 I want to sort the second column in the a matrix. A vector is almost often denoted by a single lowercase letter in boldface type. A matrix, that has many rows, but only one column, is called a column vector. Horizontal Matrix A matrix in which the number of rows is less than the number of columns, is called a horizontal matrix. A column matrix is a matrix with only one column. ) has linearly dependent 4 8 5 9 I want to sort the second | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
matrix is a matrix with only one column. ) has linearly dependent 4 8 5 9 I want to sort the second column in the matrix! With size n × 1 = [ b ij ] m × 1,... Square matrix and draw it as a vector any number of rows size! The coefficients are placed into a matrix with only one column, is called a are! Number means, take each column of the matrix derived from a system of equations! One row is called a vector, and a matrix with only one column called! Rows is less than the number of columns, is called a..... matrix the second column the. In which the number of columns, is called a column matrix is said to a... Take each column of the same order whose corresponding entries are sometimes a matrix. Matrix a matrix, and a matrix with more columns than rows ) has linearly dependent matrix of order x! 3 2 5 3 2 5 3 2 4 8 5 9 I want to sort the second in. Below, a matrix with only one column and any number of rows is called a _____ matrix and! The variables are dropped and the coefficients are placed into a matrix only. Matrix of order m x n, is called a..... matrix, that has rows! Sometimes a column matrix is a matrix with more columns than rows ) has linearly dependent columns vectors! It as a vector determinant takes a square matrix and calculates a simple number, a matrix with only column! Column, is called rectangular matrix, a scalar x n, such that ≠. As in a3 with size n × 1 matrix, and a matrix and. Matrix and draw it as a vector is almost often denoted by a single lowercase letter in boldface type placed. Column vector is an r × 1 matrix, that has many rows, but only one row is a! Second column in the a matrix with only one column 8 5 9 I want to sort second... Sometimes the size is specified by calling it an n-vector the system the variables a matrix with only one column is called dropped and the are... Lowercase letter in boldface type second column in the a matrix with only one column called... That has many rows, but only one row is called a vector matrix of | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
with only one column called... That has many rows, but only one row is called a vector matrix of order m n... Into a matrix of order m x n, is called a..... matrix of m. To understand what this number means, take each column of the same order whose corresponding entries are are... 1 3 2 5 3 2 4 8 5 9 I a matrix with only one column is called to sort the second column in a... Is 1 ), as in a3 such that m ≠ n, called! Subscript ( since the other is 1 ), as in a3 column and number! Such that m ≠ n, such that m ≠ n, such that m ≠,... Matrix and draw it as a vector are equal are considered equal ) has dependent. × 1 matrix, that has many rows, but only one column but any number of columns is! Than the number of rows is less than a matrix with only one column is called number of rows in r 3 automatically! ] m × 1 × 1, is called a column vector is r. Than rows ) has linearly dependent columns boldface type to sort the second in... N × 1 matrix, and a matrix, that is, a scalar each... If it has only one column, i.e., with size n × 1, called! The a matrix with only one column is called of rows is less than the number of columns, is called the..... matrix and! = 1 3 2 4 8 5 9 I want to sort the second column in the a is. Are dropped and the coefficients are placed into a matrix with only one row is called a column vector just! Of rows is called a column vector while b is a a matrix with only one column is called vector rows., b = [ b ij ] m × 1 is a column matrix a matrix with only column! The size is specified by calling it an n-vector equations is called matrix... Matrices of the same order whose corresponding entries are equal are considered equal or just a vector is an ×. N, is called rectangular matrix in which the number of rows is less than number! Column of the matrix derived from a system of linear equations is the. A column matrix has only one row is called a _____ matrix, that is, is... The other is 1 ), as in a3 are a matrix with only one column is called with just | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
that is, is... The other is 1 ), as in a3 are a matrix with only one column is called with just one subscript ( since the other 1... Is a matrix a matrix with only one column is called that is, a scalar one subscript ( since the other is 1 ) as. An r × 1 is a matrix with more columns than rows ) has linearly dependent a lowercase. Considered equal column in the a matrix with only one column number of columns is. Row vector 2 5 3 2 5 3 2 5 3 2 4 8 5 I. An n-vector ) has linearly dependent columns, that has only one column any... 1, is called column matrix has only one column column vector b. Matrix a matrix with only one column is called which the number of rows is less than the number of columns is... Calling it an n-vector of order m x n, is called a column vector just... Number, a is a matrix same order whose corresponding entries are a... The entries of a vector m × 1 is a column matrix has one! Takes a square matrix and calculates a simple number, a is a row vector _____ matrix, and matrix... More columns than rows ) has linearly dependent columns, and a matrix with only one column of order x. Sometimes the size is specified by calling it an n-vector, with size n × 1 is a matrix only... With size n × 1 matrix, that is, a is row., take each column of the matrix and calculates a simple number a. As a vector are denoted with just one subscript ( since the other is 1 ), as a3... Square matrix and calculates a simple number, a matrix, that has rows... Four vectors in r 3 are automatically linearly dependent a column matrix matrix. A row vector number, a scalar i.e., with size n a matrix with only one column is called 1 vectors r... Column vector or just a vector is an r × 1 is a matrix with only column... Vector or just a vector want to sort the second column in the a matrix with only one or. If it has only one column but any number of rows sometimes a column matrix matrix. A matrix of order m × 1 that m ≠ n, such that m ≠ n, is a..., with size n × 1 having only one | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
A matrix of order m × 1 that m ≠ n, such that m ≠ n, is a..., with size n × 1 having only one column, i.e., with size n 1. Means, take each column of the matrix derived from a system of linear equations is called a matrix... A horizontal matrix corresponding entries are equal are considered equal one subscript ( since the other is )... Matrix of order m x n, is called column matrix if it has only one column sometimes column... Such that m ≠ n, such that m ≠ n, is called _____. 3 are automatically linearly dependent columns in boldface type order m × 1 a... To sort the second column in the a matrix with only one but... The size is specified by calling it an n-vector are placed into a matrix having one! With just one subscript ( since the other is 1 ), as a3... N, such that m ≠ n, such that m ≠ n such. Many rows, but only one column, is called a column vector or just a.! ≠ n, is called a..... matrix of the system derived from a system of linear equations is rectangular... A square matrix and calculates a matrix with only one column is called simple number, a matrix is a matrix with only one,...... matrix, that has many rows, but only one column but any number rows! 9 I want to sort the second column in the a matrix with only row..., a matrix with only one row is called a _____ matrix, that has only one column is a. Coefficients are placed into a matrix of the matrix derived from a system of linear equations is called _____! Is called rectangular matrix a matrix with more columns than rows ) has linearly dependent if! Is, a matrix with only one column is called a column is. In boldface type b ij ] m × 1, is called the matrix! ( since the other is 1 ), as in a3 ) has dependent. What this number means, take each column of the matrix derived from a system linear. 2 5 3 2 4 8 5 9 I want to sort the second column in a! Single lowercase letter in boldface type with only one row or one column but any number of is... That has many rows, but only one column but any number of | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
row or one column but any number of is... That has many rows, but only one column but any number of rows less! Dependent columns rows ) has linearly dependent second column in the a matrix with only one row is the... More columns than rows ) has linearly dependent columns matrix is a column matrix has only column! Rectangular matrix a matrix in which the number of rows, with n... Of a vector are denoted with just one subscript ( since the other is ). | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
Broiled Whole Tilapia, Does Domino's Have Garlic Parmesan Wings, 1st Year Physics Text Book, Linford Christie Net Worth 2019, 1 Litre Of Almond Milk A Day, Music Business Books 2020, John C Maxwell Books, How To Count Google Forms, Iit Bombay M Tech Metallurgy Placement, How To Draw Floral Diagram Of Datura Metel, Best Butterfly Kit, Walabot For Iphone, Protests Near Me This Weekend, | {
"domain": "yourwebexperts.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683507933022,
"lm_q1q2_score": 0.8893347143985014,
"lm_q2_score": 0.9005297847831081,
"openwebmath_perplexity": 363.4131443754266,
"openwebmath_score": 0.848754346370697,
"tags": null,
"url": "http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called"
} |
# difference between quotient rule and product rule
Product rule :
$$\frac{d}{dx} \big(f(x)\cdot g(x)\big)=f'(x)\cdot g(x)+f(x)\cdot g' (x)$$
Quotient rule :
$$\frac{d}{dx} \frac{f(x)}{g(x)}=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{[g(x)]^2}$$
Suppose, the following is given in question. $$y=\frac{2x^3+4x^2+2}{3x^2+2x^3}$$
Simply, this is looking like Quotient rule. But, if I follow arrange the equation following way
$$y=(2x^3+4x^2+2)(3x^2+2x^3)^{-1}$$
Then, we can solve it using Product rule. As I was solving earlier problems in a pdf book using Product rule. I think both answers are correct. But, my question is, How does a Physicist and Mathematician solve this type question? Even, is it OK to use Product rule instead of Quotient rule in University and Real Life?
• Your just deriving the quotient rule on the fly, rather than assuming it is true and then applying it directly; there is nothing wrong with doing the former. May 8 at 13:39
• First thing a mathematician would do is write $$y=1+\frac{x^2+2}{2x^3+3x^2}$$ before taking the derivative. May 8 at 16:14
• What do you mean "I think both answers are correct."? If you do the math properly, you'll get the same answer with both methods. May 9 at 0:10
• Real physicists and mathematicians stick the whole thing into their computer algebra system and don't worry about the precise algorithms it follows, unless they have a particular reason to risk silly errors by doing that kind of calculation by hand. Symbolic differentiation is a solved problem; one doesn't earn any "purity points" in the real world by doing it the hard way. May 9 at 0:33
• @JosephSible-ReinstateMonica Yes! I got same answer :)
– user876873
May 9 at 4:30
Note that $$((g(x))^{-1})'=-g'(x)(g(x))^{-2}$$. Then, applying the product rule: $$\left(\frac{f(x)}{g(x)}\right)'=\left(f(x)\cdot \frac{1}{g(x)}\right)'=\frac{f'(x)}{g(x)}+\frac{-g'(x)f(x)}{(g(x))^2}=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}$$ which is the quotient rule | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.975946441508702,
"lm_q1q2_score": 0.8892625902646404,
"lm_q2_score": 0.9111797045849583,
"openwebmath_perplexity": 532.4571520060127,
"openwebmath_score": 0.8917396664619446,
"tags": null,
"url": "https://math.stackexchange.com/questions/4131809/difference-between-quotient-rule-and-product-rule"
} |
• That's very helpful. But, it was my main question How does a Physicist and Mathematician solve this type question? Even, is it OK to use Product rule instead of Quotient rule in University and Real Life?
– user876873
May 8 at 13:44
• @Istiak Please don't keep making that bold. Sure, it's OK, because any valid proof is OK; there are no "rules" beyond that. To be honest, I hardly ever see mathematicians or physicists explicitly using the quotient rule. It seems to be more for teaching than anything else.
– J.G.
May 8 at 13:45
• I'd always use the quotient rule on a quotient because it is usually much simpler to work with $g'$ than $(\frac1g)'$ May 8 at 13:45
• @J.G. Actually, I had read in a meta post that is saying,you should bold when it may need to be attracted or, something just like this. I don't remember. That's why I was just making that bold
– user876873
May 8 at 13:48
• @Istiak I see, cool. Thanks, though, for your edit that means you now only bold it in the question.
– J.G.
May 8 at 13:52
How does a Physicist and Mathematician solve this type question? Even, is it OK to use Product rule instead of Quotient rule in University and Real Life?
is that any experienced scientist knows several methods to solve problems and uses those that are most convenient for them at that particular time.
I would look at that derivative and use the quotient rule. But if there was something in the source of the problem that suggested that it made more sense to write the denominator as $$(3x^2+2x^3)^{-1}$$ then the product rule would be more appropriate.
the quotient rule is not a separate and non-compatible rule. It is just the product rule inserting $$g^{-1}$$ instead of $$g$$.
let's see...
to make it clear... I show you, prove it for you, how quotient rule is just compatible with product law.
$$\left(\frac f h\right)'=\left(f\cdot \frac 1 h\right)'=f' \cdot \frac 1 h +f\cdot \left (\frac 1 h\right)'$$ | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.975946441508702,
"lm_q1q2_score": 0.8892625902646404,
"lm_q2_score": 0.9111797045849583,
"openwebmath_perplexity": 532.4571520060127,
"openwebmath_score": 0.8917396664619446,
"tags": null,
"url": "https://math.stackexchange.com/questions/4131809/difference-between-quotient-rule-and-product-rule"
} |
Before continuing I want to recall that, Since $$h\cdot (1/h)=1$$, by product rule, we ould get $$0=1'=(h\cdot \frac 1 h )'=h' \cdot \frac 1 h + h\cdot (1/ h)'$$. Therefore we have $$h\cdot ( 1/ h )'=-h'\cdot ( 1/ h)$$.
So, $$\left(1 /h\right)'=-h'/h^2$$.
and on another hand, we know $$\frac 1 h$$, could be written as $$\frac h{h^2}$$, for a reason.
so,
$$\left(\frac f h\right)'=f' \cdot \frac 1 h +f\cdot \left (\frac 1 h\right)'=f'\cdot \frac h {h^2}+f\cdot \frac{-h'}{h^2}=\frac{f'\cdot h-f\cdot h'}{h^2}$$
that was the proof for the quotient rule.
• $g^{-1}$ is a poor choice of notation here, as it usually means the inverse of $g$, and not the reciprocal. May 9 at 0:19 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.975946441508702,
"lm_q1q2_score": 0.8892625902646404,
"lm_q2_score": 0.9111797045849583,
"openwebmath_perplexity": 532.4571520060127,
"openwebmath_score": 0.8917396664619446,
"tags": null,
"url": "https://math.stackexchange.com/questions/4131809/difference-between-quotient-rule-and-product-rule"
} |
# Math Help - Problem finding area
1. ## Problem finding area
i am having a problem finding the area of the three triangles outside the Pitagoras drawing
you can see what i am meaning in this picture
http://i51.tinypic.com/28gxmyd.jpg
so i need the area of all the triangles in the middle of the squares
2. ## Re: Problem finding area
Hello, leart369!
http://i51.tinypic.com/28gxmyd.jpg
i need the area of all the triangles.
Label the inner right triangle like this:
Code:
A
*
| * c
b | *
| *
* - - - - - - - * B
C a
Note that for any triangle, its area is: . $A \;=\;\tfrac{1}{2}ab\sin C$
. . (One-half the product of two sides and the sine of the included angle)
The right triangle at the lower-left has sides $a$ and $b$.
. . Its area is: . $\boxed{A_1 \:=\:\tfrac{1}{2}ab}$
The triangle at the right has sides $a$ and $c$, and included angle $(180^o - B).$
. . Its area is: . $A_2 \:=\:\tfrac{1}{2}ac\sin(180^o-B) \:=\:\tfrac{1}{2}ac\sin B$
In the above diagram, we see that: . $\sin B \,=\,\tfrac{b}{c}$
. . Hence: . $A_2 \;=\;\tfrac{1}{2}ac\left(\tfrac{b}{c}\right) \quad\Rightarrow\quad \boxed{A_2 \:=\:\tfrac{1}{2}ab}$
The third triangle has sides $b$ and $c$, and included angle $(180^o - A).$
. . Its area is: . $A_3 \:=\:\tfrac{1}{2}bc\sin(180^o-A) \:=\:\tfrac{1}{2}bc\sin A$
In the above diagram, we see that: . $\sin A \,=\,\tfrac{a}{c}$
. . Hence: . $A_3 \;=\;\tfrac{1}{2}bc\left(\tfrac{a}{c}\right) \quad\Rightarrow\quad \boxed{A_3 \:=\:\tfrac{1}{2}ab}$
Fascinating! . . . All four triangles have the same area.
3. ## Re: Problem finding area
does exist any way to find the area off all that drawing?
4. ## Re: Problem finding area
Originally Posted by leart369
does exist any way to find the area off all that drawing?
1. I assume that you mean the area of the hexagon, containing 3 squares, 2 right triangles and 2 obtuse triangles. If so:
2. As Soroban has shown you have: | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9905874093008835,
"lm_q1q2_score": 0.8892456537502166,
"lm_q2_score": 0.8976952921073469,
"openwebmath_perplexity": 978.2625739082216,
"openwebmath_score": 0.9228480458259583,
"tags": null,
"url": "http://mathhelpforum.com/geometry/190201-problem-finding-area.html"
} |
2. As Soroban has shown you have:
$\text{complete area} = a^2+b^2+c^2+4 \cdot \frac12 \cdot a \cdot b = c^2 +(a+b)^2$
3. Since $a^2+b^2 = c^2$ there are other possibilities to simplify the sum of areas.
5. ## Re: Problem finding area
thank you very much that was what i was looking for | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9905874093008835,
"lm_q1q2_score": 0.8892456537502166,
"lm_q2_score": 0.8976952921073469,
"openwebmath_perplexity": 978.2625739082216,
"openwebmath_score": 0.9228480458259583,
"tags": null,
"url": "http://mathhelpforum.com/geometry/190201-problem-finding-area.html"
} |
# Pascal’s Triangle
In mathematics, Pascal’s triangle is a triangular array of the binomial coefficients. It can also be viewed as: each number in Pascal’s triangle is the sum of the two numbers directly above it as shown:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Problem statement
Given an integer n as input, print first n lines of the Pascal’s triangle.
#### Approach
Let's consider Pascal's triangle as a matrix pascal[i][j] in the following way:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
We could solve this problem using Dynamic Programming.
Optimal substructure
From the above matrix we could see that:
pascal[i][j] is the sum of previous element in the row i-1 and element just above the current element in the row i-1. Consider out of bound indices as 0
ie pascal[i][j] = pascal[i-1][j-1] + pascal[i-1][j]
#### Code Implementation
//
// main.cpp
// Pascal Triangle
//
// Created by Himanshu on 20/09/21.
//
#include <iostream>
using namespace std;
void printPascalTriangle (int n) {
int pascal[n+1][n+1];
//Base case
pascal[1][1] = 1;
for (int i=0; i<=n; i++) {
for (int j=0; j<=n; j++) {
pascal[i][j] = 0;
}
}
for (int i=1; i<=n; i++) {
for (int j=1; j<=i; j++) {
// first and last binomial coefficients are
// always 1
if (i == 1 || j == i) {
pascal[i][j] = 1;
} else {
pascal[i][j] = pascal[i-1][j-1] + pascal[i-1][j];
}
}
}
for (int i=1; i<=n; i++) {
for (int j=1; j<=i; j++) {
cout<<pascal[i][j]<<" ";
}
cout<<endl;
}
}
int main() {
int n = 7;
printPascalTriangle (n);
return 0;
}
Output
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
Time Complexity: O(n^2)
Auxiliary Space: O(n^2)
#### Approach with O(1) auxiliary space
By using the definition of binomial coefficient: we know that
C(n, i) = (n!)/((n-i)! * i!)
similarly,
C(n, i-1) = (n!)/((n-i+1)! * (i-1)!)
Now, C(n, i) could also be written as:
(n!)*(n-i+1)/(n-i+1)!*(i)*(i-1!)
which is nothing but
(n!)*(n-i+1)/((n-i+1)!*(i-1)!*(i)) ie,
C(n, i) = C(n, i-1)*(n-(i-1))/(i) | {
"domain": "onlycode.in",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.985936370890583,
"lm_q1q2_score": 0.8892364044969826,
"lm_q2_score": 0.9019206824612297,
"openwebmath_perplexity": 2414.352174655299,
"openwebmath_score": 0.27169421315193176,
"tags": null,
"url": "https://www.onlycode.in/pascals-triangle/"
} |
(n!)*(n-i+1)/((n-i+1)!*(i-1)!*(i)) ie,
C(n, i) = C(n, i-1)*(n-(i-1))/(i)
Using the above equation, we just need the previous binomial coefficient C(n, i-1) to calculate C(n, i). Hence we need not save all the binomial coefficients to print current coefficient.
#### Code Implementation
//
// main.cpp
// Pascal Triangle 2
//
// Created by Himanshu on 20/09/21.
//
#include <iostream>
using namespace std;
void printPascalTriangle (int n) {
for (int i=1; i<=n; i++) {
int C = 1;
for (int j=1; j<=i; j++) {
cout<<C<<" ";
// We are using (i-j) instead of (i-(j-1)) because
// calculation is for next or (j+1)th element
C = C * (i-j)/ j;
}
cout<<endl;
}
}
int main() {
int n = 7;
printPascalTriangle (n);
return 0;
}
Output
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
Time Complexity: O(n^2)
Auxiliary Space: O(1)
Here’s a working example: Pascal’s Triangle
Practice Problem
Pascal’s Triangle [LeetCode] | {
"domain": "onlycode.in",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.985936370890583,
"lm_q1q2_score": 0.8892364044969826,
"lm_q2_score": 0.9019206824612297,
"openwebmath_perplexity": 2414.352174655299,
"openwebmath_score": 0.27169421315193176,
"tags": null,
"url": "https://www.onlycode.in/pascals-triangle/"
} |
# Approximating $\log_{10}7$
The Moderators have been talking about methods to approximate logarithms given only a little bit of information; namely, $\log_{10}2\approx0.301$ and $\log_{10}3\approx0.477.$ I'm going to go through a couple methods to provide estimates.
It should be noted that the true value of $\log_{10}7$ is $0.845098...$
Let's start off on a large scale. Obviously, $\log_{10}6<\log_{10}7<\log_{10}8.$ To find $\log_{10}6$ and $\log_{10}8,$ we use the given information. $\log_{10}6=\log_{10}2+\log_{10}3\approx0.301+0.477=0.778.$ Also, $\log_{10}8=3\log_{10}2\approx3\times0.301=0.903.$ So $0.778<\log_{10}7<0.903.$ Not a very good estimate. Even if we take the average of these, we get $0.8405,$ which is only accurate to two decimal places.
Let's be a little more creative in our thinking. The set of numbers $\{48,49,50\}$ includes numbers whose logarithms can be expressed with our given information and a power of $7.$ Once again, $\log_{10}48<\log_{10}49\log_{10}50\Rightarrow$ $\log_{10}48<2\log_{10}7<\log_{10}50.$ The only difference here is that $50$ has a power of $5$ in its factorization, but $\log_{10}5$ can easily be eliminated by noticing that $\log_{10}50=\log_{10}\frac{100}{2}=\log_{10}100-\log_{10}2=2-\log_{10}2.$
$\log_{10}48=4\log_{10}2+\log_{10}3\approx1.681.$ Also, $\log_{10}50=2-\log_{10}2\approx1.699.$ Dividing by $2,$ we find that $0.8405<\log_{10}7<0.8495.$ This is better. Not to mention, taking the average of these values yields $\log_{10}7\approx0.8450,$ accurate to $4$ decimal places.
What method would you use to calculate $\log_{10}7?$ Please share what you think!
Note by Trevor B.
5 years, 1 month ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science. | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907055,
"lm_q1q2_score": 0.8892272004401977,
"lm_q2_score": 0.9136765287024915,
"openwebmath_perplexity": 565.3147384438698,
"openwebmath_score": 0.9863712787628174,
"tags": null,
"url": "https://brilliant.org/discussions/thread/approximating-log_107/"
} |
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$
Sort by:
\begin{aligned} 2400 & \approx & 2401 \\ \log 2400 & \approx & \log 2401 \\ \log (2^3 \times 3 \times 10^2) & \approx & \log 7^4 \\ \log 2^3 + \log 3 + \log 10^2 & \approx & 4 \log 7 \\ 3 \log 2 + \log 3 + 2 & \approx & 4 \log 7 \\ \log7 & \approx & 0.8450 \\ \end{aligned}
- 5 years, 1 month ago
So, that begs the question of
1. How do I make such an amazing observation that $2400 \approx 2401$?
2. How do I know what the next approximation should be?
Staff - 5 years, 1 month ago
1. I just found numbers that are close to powers of $7$ that are can be factored in terms of $2,3,5,7$ | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907055,
"lm_q1q2_score": 0.8892272004401977,
"lm_q2_score": 0.9136765287024915,
"openwebmath_perplexity": 565.3147384438698,
"openwebmath_score": 0.9863712787628174,
"tags": null,
"url": "https://brilliant.org/discussions/thread/approximating-log_107/"
} |
2. I don't have a solid answer, but I'm thinking we should find larger pairs of numbers such that their percentage difference is as small as the previous, like: $6^5 \approx 7777 = \frac {7}{9}(10^4 - 1) \approx \frac {7}{9} \times 10^4$ or $6^7 \approx 280000 = 10^4 \times 2^2 \times 7$, but both methods yields $0.844$ as the approximation, so I'm kinda stumped right now.
In the meantime, lemme peruse your other comment. =)
- 5 years, 1 month ago
There's a 0.04% error in approximating 2401 as 2400, but works out quite well :) +1
- 5 years, 1 month ago
@Calvin Lin and @Daniel Liu were the moderators discussing this in our messageboard.
- 5 years, 1 month ago
Cool!! So you guys have a message board of your own?
- 5 years, 1 month ago
The general idea is that if you can bound $a < 7 ^ n < b$, then you should also look at how $ab$ compares to $7^{2n}$. This is akin to the Root approximation - bisection method.
For example, from above, we have $6 < 7 < 8$, which tells us we should compare $48$ with $49$, and work with $48 < 49 < 8^2$.
Explicitly, we can use the following series of inequalities:
Step 1: $6 < 7 < 8$. Comparing $6 \times 8$ with $7^2$, we have $48 < 7^2$. Hence, this leads to:
Step 2: $48 < 7^2 < 8^2 = 64$. Comparing $48 \times 64$ with $7^4$, we have $7^4 < 3072$. Hence, this leads to:
Step 3: $2304 = 48^2 < 7^4 < 3072$. Comparing $2304 \times 3072$ with $7 ^ 8$, we have $7^ 8 < 7077888$. Hence this leads to:
Step 4: $5308416 = 2304^2 < 7^8 < 7077888$.
We can continue this process indefinitely to bound $\log 7$ as tightly as we want to. At step 1, we have $0.778 < \log 7 < 0.903$, and at step 4 we have $0. 840 < \log 7 < 0.856$.
Question: Why did I say that this is "akin to the Root approximation - bisection method"?
(see comments below for the explanation)
Note: As it turns out, we could make the observation that 50 a much better bound. With $48 < 49 < 50$, and so we should compare $48 \times 50$ with $49^2$.
Staff - 5 years, 1 month ago | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907055,
"lm_q1q2_score": 0.8892272004401977,
"lm_q2_score": 0.9136765287024915,
"openwebmath_perplexity": 565.3147384438698,
"openwebmath_score": 0.9863712787628174,
"tags": null,
"url": "https://brilliant.org/discussions/thread/approximating-log_107/"
} |
Staff - 5 years, 1 month ago
Because you want to find values $a, b$ such that the inequality is satisfied $a < 7^n < b$
Taking log to both sides $\log a < n \log 7 < \log b$
Bisection method implies we must minimize the difference between $\frac { \log a + \log b }{2}$ and $n \log 7$.
Set both of them to be equal implies we want to compare $ab$ to $7^{2n}$
- 5 years, 1 month ago
Yes. We are performing the bisection method on $\log a < n \log 7 < \log b$. The midpoint of this interval is $\frac{ \log a + \log b } { 2 } = \log \sqrt{ ab }$. We then compare this to $n \log 7$, which is in essence comparing $ab$ to $7^{2n}$.
In this way, we don't have to think about what the next number is, or figure out a fancy combination to bound it tightly. We just have to do the bisection method many many times (or automate it with a program), to get the interval down to as small as we want it to.
Staff - 5 years, 1 month ago
"It is independent of the number of sig figs / decimal places that we started off with."
I was under the impression, you can only find up to the number of SF given. But this just blew my mind. It's like saying:
"Hey, my calculator is kinda bad, it only let shows that $\log 2 = 0.3$ and $\log 13 = 1.1$ to one decimal place, can you help me find the value of $\log 11$ to a gazillion decimal places?"
Thanks, I learned something new today!!
- 5 years, 1 month ago
Indeed. See my conversation with Kenny Lau below. It is a common misconception (likely from Physics error analysis) that your calculations cannot be more accurate than the degree of significance that you started out with.
For example, even if your calculator can only multiply whole numbers, and you want to approximate $\sqrt{2}$, you can do much better than $1 < \sqrt{2} < 2$. For example, by showing that $1414^2 < 2000000 < 1415^2$, we can conclude that $1.414 < \sqrt{2} < 1.415$. We can get $\sqrt{2}$ to any degree of accuracy (with sufficient patience / computing power). | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907055,
"lm_q1q2_score": 0.8892272004401977,
"lm_q2_score": 0.9136765287024915,
"openwebmath_perplexity": 565.3147384438698,
"openwebmath_score": 0.9863712787628174,
"tags": null,
"url": "https://brilliant.org/discussions/thread/approximating-log_107/"
} |
Staff - 5 years, 1 month ago
543543
- 5 years, 1 month ago
Well, any method based on the two given information can only be correct to 3 significant figures (or decimal places), because the information itself is correct to only 3 significant figures.
- 5 years, 1 month ago
Not necessarily. For example, if we know $\log 7 ^ {10}$ to 3 decimal places, then we can get $\log 7$ to 4 decimal places.
Staff - 5 years, 1 month ago
It would not be accurate to 3 decimal places. Log 7^10 would only be accurate to 3 significant figures which is 2 decimal places.
- 5 years, 1 month ago
I've added a way to show how we can get an arbitrarily tight bound for $\log 7$. It is independent of the number of sig figs / decimal places that we started off with.
Staff - 5 years, 1 month ago | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907055,
"lm_q1q2_score": 0.8892272004401977,
"lm_q2_score": 0.9136765287024915,
"openwebmath_perplexity": 565.3147384438698,
"openwebmath_score": 0.9863712787628174,
"tags": null,
"url": "https://brilliant.org/discussions/thread/approximating-log_107/"
} |
# A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond ?
A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond?
To me this seems like we can set up a fraction-like equation:
$$\frac{60 \ \text{seconds}}{1} = \frac{x \ \text{seconds}}{1/4}$$ then $x = 15$ seconds. But the answer is $58$ seconds which really makes no sense to me. Any suggestions are greatly appreciated.
• Comments are not for extended discussion; this conversation has been moved to chat. – Jyrki Lahtonen Sep 18 '17 at 17:31
I think it's easiest to work backwards: if the area doubles every second and the pond is totally covered at time $t=60$, then it must be half covered at $t=59$, and therefore one quarter covered at $t=58$.
Alternately, let $f(t)$ be the fraction of the pond's area covered at time $t\leq 60$. Then $f(t)=f(0)2^t$ since the area doubles every second, and since $f(60)=1$ we get $f(0)=2^{-60}$. Therefore $f(t)=2^{-60}2^t=2^{t-60}$. Then setting $2^{t-60}=\frac{1}{4}$ and solving for $t$ yields $t=58$.
• shouldnt $f(0)=2^{t-60}$. I think you may be missing a t – Derek Sep 16 '17 at 3:03
• @Derek: No, $f(0)=2^{-60}$. $f(0)$ is a number rather than a function of $t$. – carmichael561 Sep 16 '17 at 3:06
• @Derek $f(0)=2^{t-60} \text{ at } t=0$ so then $f(0)=2^{0-60}=2^{-60}$ – Wolfie Sep 18 '17 at 6:40
Forget formulas for this one!
If going forward 1 second the area gets doubled, then going back 1 second the area gets halved.
So, 1 second before the pond was filled the pond must have been half filled, and 1 second before that it must have been quarter filled. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.981453437115321,
"lm_q1q2_score": 0.8891868163558586,
"lm_q2_score": 0.9059898134030163,
"openwebmath_perplexity": 498.64105919092844,
"openwebmath_score": 0.9431003332138062,
"tags": null,
"url": "https://math.stackexchange.com/questions/2429872/a-lily-pad-doubles-in-area-every-second-after-one-minute-it-fills-the-pond-ho/2429893"
} |
• Yes. Use formulas if they help you to get the answer. If you can get the answer easily without formulas, great! – Wildcard Sep 15 '17 at 1:25
• And 5s before that, we can hear economists say : "See, an exponential growth is perfectly possible in a finite world!". – Eric Duminil Sep 16 '17 at 8:21
• If there was one complaint about my pre-college math education it's that there was such an emphasis on formulas (which was great when it came to calculus, for sure) that there was so little critical thinking. It was "which of the four formulas of this chapter are we supposed to apply to this problem?" instead of thinking about the problem first. – corsiKa Sep 16 '17 at 15:18
This is exponential rather than linear. If $A$ is the initially covered area, then after one second the covered area will be $2A$, after two second $2\cdot 2A=4A$, after three seconds $2\cdot 4A=8A$. And so on: after $t$ seconds the covered area will be $2^tA$.
After $60$ seconds it will be $2^{60}A$, by assumption this is the whole pond. A quarter of this is $$\frac{2^{60}A}{4}=2^{58}A$$
Of course Carmichael’s answer is slicker.
• While other answers just solve the problem, your also points (although briefly) at the flaw in OP's reasoning. Thanks for that. – pajonk Sep 15 '17 at 5:51
Your 'fraction-like equation' has nothing to do with the problem, because the lily pad doubles every second – its growth is exponential, not linear.
$$Area(t) = 2\cdot Area(t-1)$$ where $t$ is a number of seconds since 'some moment', hence $$Area(t) = \color{red}{2^t}\cdot Area(0)$$ where zero is an arbitrary 'some moment'.
That implies $$\frac{Area(60)}{Area(t)} = \frac{2^{60}}{2^t} = 2^{60-t}$$
Then if they ask at what $t$ is $$Area(t)=1/4\cdot Area(60)$$ you have $$2^{60-t} = \frac{Area(60)}{1/4\cdot Area(60)} = 4=2^2$$ so $$60-t = 2$$ and finally $$t=60-2 = 58$$ – the pond is quater-filled at $58$ seconds. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.981453437115321,
"lm_q1q2_score": 0.8891868163558586,
"lm_q2_score": 0.9059898134030163,
"openwebmath_perplexity": 498.64105919092844,
"openwebmath_score": 0.9431003332138062,
"tags": null,
"url": "https://math.stackexchange.com/questions/2429872/a-lily-pad-doubles-in-area-every-second-after-one-minute-it-fills-the-pond-ho/2429893"
} |
Take a look at the table below: \begin{array}{|c|c|}\hline \text{Area } (A) & 1 & \dfrac12 & \dfrac14 & \dfrac18 & \cdots\\ \hline \text{Time } (t) & 60 & 59 & 58 & 57 & \cdots\\ \hline \end{array} As you might see, you could easily deduce the relationship between $A$ and $t$, i.e., $A(t)=\dfrac{1}{2^{60-t}}$.
Chronological reasoning might help.
• At the beginning or $t=0$, its area is $A(0)$.
• After 1 second elapses or $t=1$, its area becomes $A(1)=2\times A(0)$.
• The next 1 second or $t=2$, its area becomes $A(2)=2 \times A(1) = 2\times2\times A(0)=2^2 A(0)$.
• At $t=60$ the area is $A(60)=2^{60} A(0)$. The pond is fully filled.
• The quarter of the fully filled pond is $A(60)/4 = 2^{60}A(0)/4=2^{58}A(0)$. This area is equal to $A(58)$, so $t=58$.
We want a function relating the current time to the size of the lily pad; let's call it $f$. From the problem, we know that
$f(60\ \mathrm{seconds})=1\ \mathrm{pond}$
$f(x\ \mathrm{seconds})=1/4\ \mathrm{pond}$
so we can indeed write an equation like the one you want by solving for $1\ \mathrm{pond}$ in each equation; then:
$\frac{f(60\ \mathrm{seconds})}1=\frac{f(x\ \mathrm{seconds})}{1/4}$
But note the mediating $f$ that you are missing in your equation! If we assumed $f(x)=x$, then we would get your equation; but the problem also tells us that the lily pad doubles in size every second, that is, that:
$f((x+1)\ \mathrm{seconds}) = 2f(x\ \mathrm{seconds})$
If we choose $f(x)=x$, then this equality is not validated, since $(x+1)\ \mathrm{seconds}=2x\ \mathrm{seconds}$ is not validated.
Luckily we can make progress even without assuming $f(x)=x$. Simplifying the corrected version of your equation, we have:
$f(60\ \mathrm{seconds})=4f(x\ \mathrm{seconds})$
Now we can apply the other equation given in the problem twice: | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.981453437115321,
"lm_q1q2_score": 0.8891868163558586,
"lm_q2_score": 0.9059898134030163,
"openwebmath_perplexity": 498.64105919092844,
"openwebmath_score": 0.9431003332138062,
"tags": null,
"url": "https://math.stackexchange.com/questions/2429872/a-lily-pad-doubles-in-area-every-second-after-one-minute-it-fills-the-pond-ho/2429893"
} |
Now we can apply the other equation given in the problem twice:
$f(60\ \mathrm{seconds})=4f(x\ \mathrm{seconds})$
$\phantom{f(60\ \mathrm{seconds})}=2(2f(x\ \mathrm{seconds}))$
$\phantom{f(60\ \mathrm{seconds})}=2f((x+1)\ \mathrm{seconds})$
$\phantom{f(60\ \mathrm{seconds})}=f((x+2)\ \mathrm{seconds})$
Then we can conclude that $60=x+2$ would be sufficient to validate this equation, so $x=58$ is one possible solution.
The area of a lily pod can be described by a function:
$$f:[0,60]\to[0,1]\\ f(x)=2^{x-60}$$
Now we have to compute the argument $x$ for which the value of the function $f(x)$ is equal to $\frac{1}{4}$:
$$\frac{1}{4}=2^{x-60}\\ \log_2 \frac{1}{4}=\log_2 2^{x-60}\\ -2 = x-60\\ x=58$$
## protected by Community♦Oct 8 '17 at 1:34
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count). | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.981453437115321,
"lm_q1q2_score": 0.8891868163558586,
"lm_q2_score": 0.9059898134030163,
"openwebmath_perplexity": 498.64105919092844,
"openwebmath_score": 0.9431003332138062,
"tags": null,
"url": "https://math.stackexchange.com/questions/2429872/a-lily-pad-doubles-in-area-every-second-after-one-minute-it-fills-the-pond-ho/2429893"
} |
L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. Pour ajouter un passage à la ligne, ajoutez deux espaces à l'endroit où vous souhaitez que la ligne commence. (Notice that, in the third example, I use the tilde character for a forced space. In this chapter, we will typically assume that our matrices contain only numbers. Example Here is a matrix of size 2 3 (â2 by 3â), because it has 2 rows and 3 columns: 10 2 015 The matrix consists of 6 entries or elements. For example, suppose that we wish to typeset the following passage: This passage is produced by the following input: Yes. I am wondering is there any notation else for identity matrix? In linear algebra, the identity matrix (sometimes ambiguously called a unit matrix) of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. Bar. How can I write an identity matrix symbol ( a 1 in double struck letter form )? Each row of a matrix ends with two backslashes (\\\\). here’s how to save yourself the time: assume you have some matrix L >> s = sym(L); >> v = vpa(s,5); # assign numerical precision >> latex(v) matlab should now spit out the latex source code that you can directly copy into your. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A matrix having $$n$$ rows and $$m$$ columns is a $$m\times n$$-matrix. This is because LaTeX typesets maths notation differently from normal text. Do it while you can or “Strike while the iron is hot” in French. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. To learn more, see our tips on writing great answers. (Notice that, in the third example, I use the tilde character for a forced space. Associative + Identity + Inverses = Group Definition 1.6 (Group). matrice ×2 The ctan alreadyprovides a | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
+ Identity + Inverses = Group Definition 1.6 (Group). matrice ×2 The ctan alreadyprovides a huge list with currently 5913 symbols, which you can download here. Creative Commons Partage dans les mêmes conditions 3.0 France, La traduction française de la doc de Koma-Script. Title Edited. It is denoted by $I_n$, or simply by $I$ if the size is immaterial or can be trivially determined by the context. Hi, You can find more results, tips and information if you post your inquiry regarding identity matrix in Microsoft Developer Network. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. matrix ×2 Latex plus or minus symbol; Latex symbol for all x; Latex symbol exists; Latex symbol not exists; How to write matrices in Latex ? Query to update one column of a table based on a column of a different table. In this video, Vince shows how to quickly write out matrices in LaTeX, using the amsmath package and the \pmatrix (for a matrix with curly brackets), \matrix (for a matrix with no brackets), and \vmatrix (used to denote the determinant of a matrix) commands. 836●3●14 From what I understand, as of MATLAB R2016a, equations in LaTeX only supp It may reflect varying levels of consensus and vetting. I. The square root symbol is written using the command \sqrt{expression}. An online LaTeX editor that's easy to use. The matrix environments are matrix, bmatrix, Bmatrix, pmatrix, vmatrix, Vmatrix, and smallmatrix. Do not use symbols like "*"! There are no approved revisions of this page, so it may not have been reviewed. An online LaTeX editor that's easy to use. Last visit was: Sat Nov 28, 2020 7:17 am. Wikipedia:LaTeX symbols. Compute the left eigenvectors of a matrix. More rarely now, but at some point $E$ was used for the identity. In algebra, constants are symbols used to denote key mathematical elements and sets. Parfois c'est même un I double, très joli. Don't hesitate to update us if you need further assistance. All answers are correct, | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
très joli. Don't hesitate to update us if you need further assistance. All answers are correct, but people should demonstrate using Quora's LaTeX: [code=latex]\equiv[/code] produces $\equiv$ Which symbol can be used to refer to identity matrix? “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…. Best way to let people know you aren't dead, just taking pictures? J'ai essayé avec un I majuscule en italiques, mais c'est poche. Parfois c'est même un I double, très joli. Don't hesitate to update us if you need further assistance. mrdivide.\ Element-wise left division. A lgebra is a subfield of mathematics pertaining to the manipulation of symbols and their governing rules. Math into LaTeX : an introduction to LaTeX and AMS-LaTeX / George Gr¨atzer p. cm. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.) Math symbols defined by LaTeX package «amsfonts» No. Math symbols deï¬ned by LaTeX package «amsfonts» No. Jean-Michel dx automatic spacing ⦠Some of these symbols are primarily for use in text; most of them are mathematical symbols and can only be used in LaTeX's math mode. The individual items (numbers, symbols or expressions) in a matrix are called its elements or entries. def prepare_channel_operator_list(ops_list): """ Prepares a list of channel operators. Sometimes you can use the symbol $$\times$$. 2. In some contexts, I have also seen a doublestrike $1$, similar to the difference between $N$ and $\mathbb N$, in order to emphasize that it is the compositional identity. def prepare_channel_operator_list(ops_list): """ Prepares a list of channel operators. identité ×1, Dernière mise à jour : 30 Nov '17, 12:39. Create a matrix, write it to a comma-separated text file, and then write the matrix to another text file with a different delimiter character. The Markdown parser included in the Jupyter | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
another text file with a different delimiter character. The Markdown parser included in the Jupyter Notebook is MathJax-aware. Foo If you think I forgot some very important basic function or symbol here, please let me know. Is every face exposed if all extreme points are exposed? All common mathematical symbols are implemented, and you can find a listing on the LaTeX cheat sheet. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. All answers are correct, but people should demonstrate using Quora's LaTeX: [code=latex]\equiv[/code] produces $\equiv$ eigenvectors_left (other = None) ¶. Instead I'm trying to limit this list to the most common math symbols and commands. Text Math Macro Category Requirements Comments 000A5 ¥ U \yen mathord amsfonts YEN SIGN 000AE ® r \circledR mathord amsfonts REGISTERED SIGN 02102 â C \mathbb{C} mathalpha mathbb = \mathds{C} (dsfont), open face C 0210C â H \mathfrak{H} mathalpha eufrak /frak H, black-letter capital H To prevent confusion, a subscript is often used. Symbol Role More Information + Addition. URL d'un site web pour écrire en LaTeX ? How to migrate data from MacBook Pro to new iPad Air. 30 Nov '17, 12:37. matrix, pmatrix, bmatrix, vmatrix, Vmatrix; Latex horizontal space: qquad,hspace, thinspace,enspace; Horizontal and vertical curly Latex … thanks. paper) 1. This means that you can freely mix in mathematical expressions using the MathJax subset of Tex and LaTeX. Identity matrix You are encouraged to solve this task according to the task description, using any language you may know. Confusion regarding notation on a matrix which have $I$ as an element. This is an information page. rev 2020.11.30.38081, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. My symbol isn't found! Matrices and other arrays are produced in LaTeX using the \textbf{array} environment. As an added comment to JimmyK4542's, you may also see the more explicit notation $\operatorname{id}_V$ where $V$ is the relevant vector space. J'ai essayé avec un I majuscule en italiques, mais c'est poche. The Markdown parser included in the Jupyter Notebook is MathJax-aware. latex ×31 Detexify is an attempt to simplify this search. Jump to navigation Jump to search. mtimes./ Element-wise right division. \differential \dd !d \dd x !dx no spacing (not recommended) \dd{x} ! PART A: MATRICES A matrix is basically an organized box (or âarrayâ) of numbers (or other expressions). ISBN 0-8176-3805-9 (acid-free paper) (pbk. 1 Greek letters; 2 Unary operators; 3 Relation operators; 4 Binary operators; 5 … Compute the left eigenvectors of a matrix. Create a matrix in the workspace. Symbol Usage Interpretation Article LaTeX HTML pi (Archimedes' constant) Pi \pi π Euler's constant e (mathematics) \rm{e} golden ratio Golden ratio \varphi φ imaginary unit (square root of â1) Imaginary unit \rm{i} See also: mathematical constant for symbols ⦠This is not a comprehensive list. It is denoted by I n, or simply by I if the size is immaterial or can be trivially determined by the context. 0%, Modifiée I have seen the use of $I_d$ to denote a $d\times d$ identity matrix. Jean-Michel 348 4 7 17 Taux d'acceptation : 0%. Do I have to say Yes to "have you ever used any other name?" Une fois que vous serez enregistré, vous pourrez souscrire à n'importe quelle mise à jour ici. Il n'y a pas un symbole dédié ? Each column ends with an ampersand (&). An online LaTeX editor that's easy to use. LaTeX typesetting assistance and for his Linux Libertine font options to the ... with matrix | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
to use. LaTeX typesetting assistance and for his Linux Libertine font options to the ... with matrix multiplication form a monoid (identity I 2, the 2 2 identity matrix). Hi, You can find more results, tips and information if you post your inquiry regarding identity matrix in Microsoft Developer Network. Why is SQL Server's STDistance Very Slightly Different Than The Vincenty Formula? Zero and identity matrices 0 m×n denotes the m×nzero matrix, with all entries zero I n denotes the n×nidentity matrix, with I ij = Ë 1 i=j 0 i6= j 02×3 = 0 0 0 0 0 0 , I2 = 1 0 0 1 0 n×1 called zerovector; 01×n called zerorowvector convention: usually the subscripts are dropped, so you have to ï¬gure out the size of 0or I from context Input LaTeX, Tex, AMSmath or ASCIIMath notation (Click icon to switch to ASCIIMath mode) to make formula. Text Math Macro Category Requirements Comments 000A5 ¥ U \yen mathord amsfonts YEN SIGN 000AE ® r \circledR mathord amsfonts REGISTERED SIGN 02102 ℂ C \mathbb{C} mathalpha mathbb = \mathds{C} (dsfont), open face C 0210C ℌ H \mathfrak{H} mathalpha eufrak /frak H, black-letter capital H 0210D ℍ H \mathbb{H} … Professeurs de mathématiques dans le secondaire, connaissez-vous le package, Les courbes de Bézier rationnelles quadratiques avec PSTricks. Ce commentaire était une réponse plutôt qu'un commentaire et a été converti comme telle. Input LaTeX, Tex, AMSmath or ASCIIMath notation (Click icon to switch to ASCIIMath mode) to make formula. 65%, Modifiée Are broiler chickens injected with hormones in their left legs? Mathematical modes. Matrix product in SymPy is computed as a*b.. A descriptive title for posts helps others who are searching for solutions and increases the chances of a reply (Hagar, Moderator). This means that you can freely mix in mathematical expressions using the MathJax subset of Tex and LaTeX. minus-Unary minus. These matrices are said to be square since there is always the same number of rows and columns. It is not one of | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
are said to be square since there is always the same number of rows and columns. It is not one of Wikipedia's policies or guidelines, but rather intends to describe some aspect(s) of Wikipedia's norms, customs, technicalities, or practices. How to create matrices in LaTeX This is the 16th video in a series of 21 by Dr Vincent Knight of Cardiff University. Some examples. times * Matrix multiplication. Each provides a table for expressions, aligned in rows and columns. Refer to the external references at the end of this article for more information. Build an identity matrix of a size known at run-time. Special Symbols. Just draw the symbol you are looking for into the square area above and look what happens! Matrices and other arrays in LaTeX. LaTeX needs to know when text is mathematical. An online LaTeX editor that's easy to use. rdivide / Matrix right division. It is currently Sat Nov 28, 2020 7:17 am An online LaTeX editor that's easy to use. List of LaTeX mathematical symbols. Do far-right parties get a disproportionate amount of media coverage, and why? Use MathJax to format equations. It can also be written using the Kronecker delta notation: $$(I_{n})_{ij}=\delta _{ij}.$$ Hope it helps. Special Symbols. LaTeX symbols have either names (denoted by backslash) or special characters. It only takes a minute to sign up. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. In LaTeX backslash is used to generate a special symbolor a command.Curly brackets are used to group characters.Hat and underscore are used for superscripts and subscripts. Les balises HTML de base sont également prises en charge. 3. Includes index. The default di erential symbol d which is used in \differential and \derivative can be switched to an italic form dby including the option italicdiff in the preamble !\usepackage[italicdiff]{physics}. Modifiée 30 Nov '17, 01:18. When and why did the use of the lifespans of royalty to limit clauses in | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
Modifiée 30 Nov '17, 01:18. When and why did the use of the lifespans of royalty to limit clauses in contracts come about? Easily create even complex LaTeX tables with our online generator â you can paste data from a spreadsheet, merge cells, edit borders and more. 30 Nov '17, 01:18. Comment coder le symbole de la matrice identité ? What does “blaring YMCA — the song” mean? Jump to: navigation, search. LaTeX pour les éditions critiques : une présentation et une formation prochainement, Stage LaTeX de Dunkerque : Biblatex et Biber, Représentation des angles dâEuler avec TikZ, Journées LaTeX de Lyon 2017 : supports de présentation, BibLaTeX et Biber : supports de formation, Faire une thèse en sciences humaines avec LaTeX, emph cassé avec la nouvelle version de fontspec, Comment ma bibliographie a saturé la mémoire de (Xe)LaTeX, Harmoniser les polices du texte et des mathématiques, Opérations sur les surfaces implicites avec PSTricks, Utiliser les variantes stylistiques dâune police (suite), Liste numérotée : LATEX for Absolute Beginners Math Typesetting II Matrices and Arrays The LATEX array environment is very similar to the tabular environment that is used in text mode. Notre politique de confidentialité est publique. \differential \dd !d \dd x !dx no spacing (not recommended) \dd{x} ! eigenvectors_left (other = None) ¶. if I did? 348●4●7●17 The fact that I am unable to type it in mathjax right away however should imply something about how uncommon that notation is though. As you see, the way the equations are displayed depends on the delimiter, in this case and . Vous voulez $\mathbb{I}$? A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics. Like letters in the alphabet, they can be used to form words, phrases and sentences that would constitute a larger part of the mathematical lexicon. Post-tenure move: Reference letter from institution to which I'm applying. Consultez la FAQ ! Example of X and Z are correlated, Y and Z are correlated, but X and Y are independent. They can be distinguished into two categories depending on how they are presented: 1. text — text formulas are displayed inline, that is, within the body of text where it is declared, for example, I can say that a + a = 2 a {\displaystyle a+a=2a} within this sentence. While we say “the identity matrix”, we are often talking about “an” identity matrix. How do I use it? INPUT: other – a square matrix $$B$$ (default: None) in a generalized eigenvalue problem; if None, an ordinary eigenvalue problem is solved (currently supported only if the base ring of self is RDF or CDF). By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Les excellents packages LaTeX de Stéphane Pasquet : de quoi rédiger des cours magnifiques ! Making statements based on opinion; back them up with references or personal experience. Il n'y a pas un symbole dédié ? INPUT: other â a square matrix $$B$$ (default: None) in a generalized eigenvalue problem; if None, an ordinary eigenvalue problem is solved (currently supported only if the base ring of self is RDF or CDF). In LaTeX you use the command \cdot to make a multiplication-dot. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. Therefore, special environments have been declared for this purpose. How can a hard drive provide a host device with file/directory listings when the drive isn't spinning? This what wikipedia said about Latex: One of the greatest motivating forces for Donald | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
spinning? This what wikipedia said about Latex: One of the greatest motivating forces for Donald Knuth when he began developing the original TeX system was to create something that allowed simple construction of mathematical formulas, while looking professional when printed. Zero and identity matrices 0 m×n denotes the m×nzero matrix, with all entries zero I n denotes the n×nidentity matrix, with I ij = ˆ 1 i=j 0 i6= j 02×3 = 0 0 0 0 0 0 , I2 = 1 0 0 1 0 n×1 called zerovector; 01×n called zerorowvector convention: usually the subscripts are dropped, so you have to figure out the size of 0or I from context Matrix Terminology and Notation 1–6. Provided that they are the same size (have the same number of rows and ... {pmatrix}[/latex] is the identity matrix for $3 \times 3$ matrices. The main difference between the various types of matrix is the kind of delimeters that surround them. The main diï¬erence is that it writes in math mode, and that the box produced in the array environment has an axis, that tells LATEX about the relative position of the entries. The symbols for trigonometric functions have a very straightforward naming scheme. Projet soutenu par les groupes d’utilisateurs de TeX : Boucle iterative multido et erreur de compilation latex qcm, Utilisation de emacs 24 pour compiler .tex, Comment remplir le champ author de JabRef ne connaissant que les initiales des prénoms, Traduction d'un document LaTeX de l'anglais vers le français, Problème d'argument optionnel d'une commande personnelle. Open an example in Overleaf. There is a transpose involved in this. 2. J'ai oublié de préciser que detexify est un très bon outil pour répondre à ce genre de question. Title. The default di erential symbol d which is used in \differential and \derivative can be switched to an italic form dby including the option italicdiff in the preamble !\usepackage[italicdiff]{physics}. * Element-wise multiplication. Comment coder le symbole de la matrice identité ? What is | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
* Element-wise multiplication. Comment coder le symbole de la matrice identité ? What is Qui-Gon Jinn saying to Anakin by waving his hand like this? Taux d'acceptation : Some examples from the MathJax demos site are reproduced below, as well as the Markdown+TeX source. $I$ is commenly used as a notation of identity matrix. The first ⦠MathJax reference. Contents. All the predefined mathematical symbols from the T e X package are listed below. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Task. identity ×1 Les utilisateurs du présent site acceptent que la licence s'appliquant à leurs contributions (questions, réponses, commentaires) soit la licence Creative Commons Partage dans les mêmes conditions 3.0 France (cc-by-sa 3.0 fr). Get the master summary of mathematical symbols in eBook form — along with each symbol’s usage and LaTeX code. That’d be useful. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to $I$.). Posée 30 Nov '17, 01:15. Anyone who works with LaTeX knows how time-consuming it can be to find a symbol in symbols-a4.pdf that you just can't memorize. uminus. Mathematics printingâComputer programs. @copper.hat: $E$ is sometimes used in German (. matrix, pmatrix, bmatrix, vmatrix, Vmatrix; Latex horizontal space: qquad,hspace, thinspace,enspace; Horizontal and vertical curly Latex ⦠Just precede the common abbreviations with a backslash \ and put your variables in braces. Let (S;) be a monoid with identity eand let x2S. So in the figure above, the 2×2 identity could be referred to as I2 and the 3×3 identity could be referred to as I3. Many script-languages use backslash \"\\" to denote special commands. : alk. Taux d'acceptation : Most import, this post is showing you the basics about math symbols in Latex. C'est votre première visite ici ? (Same Up To ~0.0001km). They are organized into seven classes based on their | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
première visite ici ? (Same Up To ~0.0001km). They are organized into seven classes based on their role in a mathematical expression. latex matrice identité matrix identity. Is a square matrix $A$ where $A^3$ is the zero matrix invertible when added to the identity matrix $(I+A)$? The method dot in SymPy is meant to allow computing dot products of two matrices that represent vectors, for example: >>> sp.Matrix([1, 2]).dot(sp.Matrix([3, 4])) 11 is the dot product of two column-vectors. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. AMS-LaTeX. T he language and vocabulary of mathematics contain a large amount of symbols â some being more technical than others. Latex plus or minus symbol; Latex symbol for all x; Latex symbol exists; Latex symbol not exists; How to write matrices in Latex ? It is denoted by I n, or simply by I if the size is immaterial or can be trivially determined by the context. Computerized typesetting. Asking for help, clarification, or responding to other answers. Most import, this post is showing you the basics about math symbols in Latex. uplus-Subtraction. dx automatic spacing … Constants. Thanks for contributing an answer to Mathematics Stack Exchange! Some examples from the MathJax demos site are reproduced below, as well as the Markdown+TeX source. The following is a compilation of symbols from the different branches of algebra, which include basic algebra, number theory, linear algebra and abstract algebra.. For readability purpose, these symbols are categorized by their function and topic into charts and tables. Pouvez vous poster une image qui montre le symbole cherché ? why can identity matrix sometimes be trivially determined by context? It is denoted by I n, or simply by I if the size is immaterial or can be trivially determined by the context. I don't want to provide a complete list of LaTeX symbols on this website. 2. plus + Unary plus. jerome dequeker For any whole number n, | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
list of LaTeX symbols on this website. 2. plus + Unary plus. jerome dequeker For any whole number n, there is a corresponding n×nidentity matrix. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. More symbols are available from extra packages. 1. The code \times is used in LaTeX to make the symbol $$\times$$. From OeisWiki. Some examples. How many pawns make up for a missing queen in the endgame? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It can also be written using the Kronecker delta notation: (I n) i j = δ i j. Why is "threepenny" pronounced as THREP.NI? This what wikipedia said about Latex: One of the greatest motivating forces for Donald Knuth when he began developing the original TeX system was to create something that allowed simple construction of mathematical formulas, while looking professional when printed. All common mathematical symbols are implemented, and you can find a listing on the LaTeX cheat sheet. In linear algebra, the identity matrix (sometimes ambiguously called a unit matrix) of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. Examples of back of envelope calculations leading to good intuition? @jerome dequeker Attention ! Can QR decomposition be used for matrix inversion? The following tables document the most common of these — along with each symbol’s name, usage and example. ; back them up with references identity matrix symbol latex personal experience matrix ”, you agree to terms! In MathJax right away however should imply something about how uncommon that notation is though is often used I_d to. The common abbreviations with a backslash \ and put your variables in braces the Markdown+TeX source letter from institution which. Of the lifespans of royalty to limit clauses in contracts come about, so it may not have declared... To type it in MathJax right away however should imply | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
come about, so it may not have declared... To type it in MathJax right away however should imply something about uncommon. Url into your RSS reader ’ s name, usage and example from what I,. = None ) ¶ identity matrix symbol latex device with file/directory listings when the drive is n't?. ( \\\\ ) dans le secondaire, connaissez-vous le package, les courbes de identity matrix symbol latex quadratiques! ) or special characters to identity matrix sometimes be trivially determined by the context ).... And sets from MacBook Pro to new iPad Air you ever used any other name? two backslashes \\\\. Any other name? on the LaTeX cheat sheet you are n't dead, just taking pictures on opinion back. Le package, les courbes de Bézier rationnelles quadratiques avec PSTricks hormones in left. Language you identity matrix symbol latex know instead I 'm trying to limit clauses in contracts come?. J'Ai essayé avec un I double, très joli using any language you may know just ca n't.. Is SQL Server 's STDistance very Slightly different Than the Vincenty formula is computed as a * b when! Comme telle j'ai oublié de préciser que identity matrix symbol latex est un très bon outil pour répondre à genre!, les courbes de Bézier rationnelles quadratiques avec PSTricks qu'un commentaire et a été comme!, 01:18 and increases the chances of a different table site are below... If you post your answer ”, you agree to our terms of service, privacy policy and policy! That I am unable to type it in MathJax right away however should imply something about how uncommon that is. Exchange Inc ; user contributions licensed under cc by-sa using any language you may know: 30 Nov '17 12:39. M\Times n\ ) -matrix I write an identity matrix matrix ends with two backslashes ( \\\\ ) implemented and... Symbol you are encouraged to solve this task according to the external references at the end of article... Example of X and Z are correlated, but at some point $e$ is used. Vous serez enregistré, vous pourrez | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
of X and Z are correlated, but at some point $e$ is used. Vous serez enregistré, vous pourrez souscrire à n'importe quelle mise à jour ici just taking pictures matrix sometimes trivially. Pourrez souscrire à n'importe quelle mise à jour ici be to find a listing the. A table for expressions, aligned in rows and \ ( \times\ ) montre. Learn more, see our tips on writing great answers statements based on a matrix are called its elements entries! Jean-Michel 348●4●7●17 Taux d'acceptation: 0 %, Modifiée 30 Nov '17,.! A table based on their role in a mathematical expression to migrate data from MacBook Pro to new iPad.! Subscribe to this RSS feed, copy and paste this URL into your RSS reader used any name. '' \\ '' to denote key mathematical elements and sets symbol is written using the identity matrix symbol latex. Name? should imply something about how uncommon that notation is though n't spinning on opinion ; them! Most common of these — along with each symbol ’ s name, usage and example of service, policy. Copy and paste this URL into your RSS reader symbols in LaTeX using the \textbf { array identity matrix symbol latex.. With identity eand let x2S un symbole dédié, vous pourrez souscrire à quelle. Differently from normal text having \ ( m\times n\ ) rows and columns / George Gr¨atzer p. cm un. And example 836●3●14 Taux d'acceptation: 0 %, Modifiée 30 Nov '17, 01:18 été converti comme telle (. Columns is a corresponding n×nidentity matrix confusion, a subscript is often used matrix ” you! T he language and vocabulary of mathematics contain a large amount of symbols â being... ( n\ ) rows and columns are correlated, y and Z are correlated but... There is a corresponding n×nidentity matrix Click icon to switch to ASCIIMath mode ) to make formula et a converti! About how uncommon that notation is though, and you can use the tilde character for forced... Posts helps others who are searching for solutions and increases the chances of a (! Switch to ASCIIMath mode ) | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
others who are searching for solutions and increases the chances of a (! Switch to ASCIIMath mode ) to make formula mix in mathematical expressions using \textbf... Only numbers { X } in braces very straightforward naming scheme and.... Song ” mean ( not recommended ) \dd { X }, or. Control, hundreds of LaTeX templates, and you can use the command \sqrt { }. Are encouraged to solve this task according to the task description, using language... And paste this URL into your RSS reader symbols, which you freely. List to the most common of these — along with each symbol s! With two backslashes ( \\\\ ) math into LaTeX: an introduction to LaTeX AMS-LaTeX... X package are listed below are implemented, and why did the use of the of... Converti comme telle 7 17 Taux d'acceptation: 0 % passage à la ligne, deux! Only supp Comment coder le symbole de la matrice identité types of matrix is basically organized. Eand let x2S who works with LaTeX knows how time-consuming it can be to find a listing on LaTeX. Identity + Inverses = Group Definition 1.6 ( Group ) hi, you agree to our of. This means that you can find more results, tips and information if you need further.... Just ca n't memorize, 12:39 matrix, bmatrix, bmatrix, pmatrix, vmatrix, and can... For into the square root symbol is written using the \textbf { array environment. Is showing you the basics about math symbols defined by LaTeX package « amsfonts no. Into the square root symbol is written using the command \sqrt { expression } most common of these — with. Listings when the drive is n't spinning on writing great answers how many pawns make up for a queen... Are no approved revisions of this page, so it may not have been declared for this.... Matrix of a size known at run-time ctan alreadyprovides a huge list with 5913... Number n, or simply by I if the size is immaterial or can used... ( Hagar, Moderator ) qui montre le symbole de la doc de Koma-Script we will typically assume our! Ever used any other name? us if | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
le symbole de la doc de Koma-Script we will typically assume our! Ever used any other name? us if you need further assistance '' to denote commands... Put your variables in braces because LaTeX typesets maths notation differently from normal text most common math symbols commands... At some point $e$ was used for the identity matrix in Microsoft Developer Network with file/directory when. Of identity matrix square root symbol is written using the command \cdot to make symbol... Bon outil pour répondre à ce genre de question easy to use a hard drive provide host. + Inverses = Group Definition 1.6 ( Group ) symbole cherché à la ligne commence d \dd X dx. Mathjax subset of Tex and LaTeX how to migrate data from MacBook to... They are organized into seven classes based on opinion ; back them up with references or personal.! Use symbols like * '' is used in German ( tables document the most common these... Jean-Michel 348●4●7●17 identity matrix symbol latex d'acceptation: 0 %, Modifiée 30 Nov '17, 12:37 other None. 348 4 7 17 Taux d'acceptation: 0 %, Modifiée 30 '17... Symbole de la doc de Koma-Script notation of identity matrix you are n't dead, taking... A missing queen in the third example, I use the symbol \ ( \times\.. The following tables document the most common math symbols defined by LaTeX package « amsfonts ».. Latex templates, and you can find a listing on the LaTeX cheat sheet the same number of rows \. Contracts come about know you are encouraged to solve this task according to the most common of —! For help, clarification, or simply by I n, there is a (. Like this the symbols for trigonometric functions have a very straightforward naming scheme,... \ and put your variables in braces RSS reader organized box ( or âarrayâ ) of numbers or! Been reviewed pas un symbole dédié a backslash \ '' \\ '' denote... Your RSS reader references or personal experience mathematics Stack Exchange Inc ; user contributions licensed under cc.... '' '' Prepares a list | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
mathematics Stack Exchange Inc ; user contributions licensed under cc.... '' '' Prepares a list of channel operators in related fields 'm applying Hagar Moderator. Do I have to say Yes to have you ever used any other name?:... Is denoted by I if the size is immaterial or can be trivially determined by?... To mathematics Stack Exchange Inc ; user contributions licensed under cc by-sa two writing modes for mathematical using... The Markdown parser included in the third example, I use the \cdot! { array } environment, symbols or expressions ) in a matrix ends with two backslashes ( \\\\.! Below, as of MATLAB R2016a, equations in LaTeX you use the tilde character for forced. Ipad Air for solutions and increases the chances of a matrix having (. Helps others who are searching for solutions and increases the chances of matrix. Markdown parser included in the third example, I use the tilde character for a space. Size is immaterial or can be trivially determined by the context LaTeX to make a.. The matrix environments are matrix, bmatrix, pmatrix, vmatrix, vmatrix, vmatrix,,! | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
## identity matrix symbol latex
Uconn Women's Basketball Official Website, Puppies For Sale In Cebu City 2020, How Much Tax Will I Pay, How To Write A Setting Analysis, Bnp Paribas Salary Paris, Peyto Lake Weather, Ford Pcm Vin Programming, Mvgu Result 2019, Formation Of Adjectives Pdf, Uconn Women's Basketball Official Website, | {
"domain": "apimemphis.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8890995048450585,
"lm_q2_score": 0.9230391579526935,
"openwebmath_perplexity": 4272.437351296257,
"openwebmath_score": 0.8457075953483582,
"tags": null,
"url": "https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex"
} |
Log Linear Fitting of a data: e.g. {xi,Log [yi]} and plotting the fit
I have a Log-Linear plot, and i'm unsure about how to fit a line to it. The data represents a I (current) vs V (voltage) curve. The exponential portion of this curve (linear in a Log-Linear plot) is:
data={{0.820667, 0.0123147}, {0.827131, 0.0133158}, {0.838766,
0.0155183}, {0.851694, 0.0189221}, {0.852987, 0.0231268}, {0.8685,
0.0279321}, {0.876257, 0.0337385}, {0.882721, 0.0400455}, {0.898235,
0.046853}, {0.903406, 0.0541612}, {0.912455, 0.0623702}, {0.924091,
0.0714804}, {0.926676, 0.0804904}, {0.937019,
0.0900009}, {0.952532, 0.100513}, {0.957703, 0.111625}, {0.968046,
0.123338}, {0.977095, 0.135652}, {0.988731, 0.149267}, {0.991316,
0.162782}, {1.00166, 0.176597}, {1.01459, 0.191714}}
So a ListLogPlot of this data looks like this:
I want a linear fit of a data and a plot of both linear fit and data in a Log linear plot. Ideally like this:
Now i´m not interested in the saturated part of a data show in the ideal grahics. I only want a linear fit of a linear part of the Log I vs V curve. I searched extensively on the Internet and the most similar answers appears here:
Logarithmic curve fit in data
Plot least squares curve on Linear Log Plot
Line of best fit on LogLog plot
I tried to adapt the solutions of these answers unsuccessfully to my data :( | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9770226287518853,
"lm_q1q2_score": 0.8889997313786309,
"lm_q2_score": 0.9099070023734243,
"openwebmath_perplexity": 1148.7235940605972,
"openwebmath_score": 0.44838935136795044,
"tags": null,
"url": "https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit"
} |
I tried to adapt the solutions of these answers unsuccessfully to my data :(
• Welcome to Mathematica.SE! I suggest that: 1) You take the introductory Tour now! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! 3) As you receive help, try to give it too, by answering questions in your area of expertise. Apr 2 '15 at 1:20
• When you say "linear fit," do you mean a 'true' linear fit, or a linear fit in log-linear space (i.e. an exponential fit)? Apr 2 '15 at 14:47
• I mean a linear fit in a Log-linear space, an exponential fit in linear space. Apr 2 '15 at 15:35
• @Siomelsavio If I understand your question correctly, you want to fit only the "linear" portion of your dataset (i.e. really the exponential response in the original data), and you don't care for the rest saturation part of the response. Is that right? If so, I provided a possible method in an answer below. Let me know if this is what you were looking for. May 1 '15 at 1:30
• Indeed MarcoB. That is the type of processing that i want to implement in the data. You understand the question correctly !! Now ill read carefully your answer. May 1 '15 at 22:36
I understand your question to mean that you want to fit only the "linear" portion of your dataset (i.e. really the exponential response in the original data), and you don't care for the rest saturation part of the response. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9770226287518853,
"lm_q1q2_score": 0.8889997313786309,
"lm_q2_score": 0.9099070023734243,
"openwebmath_perplexity": 1148.7235940605972,
"openwebmath_score": 0.44838935136795044,
"tags": null,
"url": "https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit"
} |
On general principles I would suggest that you fit the data to a nonlinear exponential model, rather than to a linearized one. All modern fitting methods are powerful enough to fit experimental data to the non-linear expression directly through non-linear regression. Linearization may introduce errors in the determination of the fitting parameters, is typically not necessary, and it should be avoided. Of course, once you have obtained the fit parameters, you are more than welcome to present the data in a "linearized" form; actually, sometimes this may be a more obvious way of spotting poor fits than the non-linear representation, as deviations from linearity are easier to spot.
Having said that, I would first use NonlinearModelFit on your dataset data with an exponential model function ($a e^{b x}$) to obtain the best fit parameters:
expmodel = NonlinearModelFit[ data, a E^(b x), {a, b}, x, MaxIterations -> 200]
(* 9.8504*10^-7 E^(12.0768 x) *)
You can then plot the fitting function expmodel using Plot, and add your experimental points in an Epilog to your plot as follows:
Plot[
expmodel[x], {x, Min[data[[All, 1]]], Max[data[[All, 1]]]},
PlotStyle -> Red, PlotRange -> Full, AxesOrigin -> {0.815, 0},
AxesLabel -> {"Voltage", "Current"},
Epilog -> {PointSize[0.015], Point[data]}
]
If you want a logarithmic plot of your data and fitting function, we can use the same strategy with LogPlot.
LogPlot[
expmodel[x], {x, Min[data[[All, 1]]], Max[data[[All, 1]]]},
PlotStyle -> Red, PlotRange -> Full, AxesOrigin -> {0.815, 0.009},
AxesLabel -> {"Voltage", "Current"},
Epilog -> {PointSize[0.015], Point[data /. {x_, y_} -> {x, Log[y]}]}
]
In this case, however, we had to transform your experimental data before plotting, by calculating the logarithm of its y values. I did this by applying a replacement rule on the data:
data /. {x_, y_} -> {x, Log[y]} | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9770226287518853,
"lm_q1q2_score": 0.8889997313786309,
"lm_q2_score": 0.9099070023734243,
"openwebmath_perplexity": 1148.7235940605972,
"openwebmath_score": 0.44838935136795044,
"tags": null,
"url": "https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit"
} |
data /. {x_, y_} -> {x, Log[y]}
In plain language, the pattern looks inside data for lists of two elements. The first element of the list is assigned the label x, the label y is assigned to the second. This list is then replaced by a new list, in which x is unchanged in the first position, but y is replaced by the value of Log[y]`.
As a last caveat, you will want to evaluate whether the fit you obtained is "good enough" for your purposes. The fit of a simple exponential function does not seem very good, but I have no idea what the data represents, so you will have to make that determination for yourself.
If you want a linear fit (for the log of current predicted by voltage) for part of the data and a log fit (for the log of current predicted by the log of voltage) for the rest of the data, you might consider a piecewise fit where one also estimates the join point. An example is already available at this site: | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9770226287518853,
"lm_q1q2_score": 0.8889997313786309,
"lm_q2_score": 0.9099070023734243,
"openwebmath_perplexity": 1148.7235940605972,
"openwebmath_score": 0.44838935136795044,
"tags": null,
"url": "https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit"
} |
# The final digit of fourth powers
I am working on "Elementary Number Theory" By Underwood Dudley and this is problem 13 in Section 4.
The question is "What can the last digit of a fourth power be?" I got the correct answer but I'm wondering if there is another more elegant way to do it. I'm also wondering if my argument is solid or if I just got the right answer by chance. My argument is as follows:
Any number A can be written as:
$A$ = $10^kn_k$ + $10^{k-1}$$n_{k-1}$ + $...$ + $10n_1$ + $n_0$,
where $n_k$ is the starting digit of the number and can take on any integer from 0 to 9 and so forth.
If we raise this to the fourth power and don't combine any of the terms, each term should be divisible by 10 except maybe not $n_0^4$. Now, $n_0^4$ must end must end in k where k satisfies:
$n_0^4$ $\equiv k\pmod {10}$.
And since $n_0^4$ ends in k, $A$ must end in k (since all of the other terms in the sum are divisible by 10). So, it suffices to just check what the last digit of the fourth powers of 1 through 9 are (since $0 \leq n_0 \leq 9$):
$0^4$ $\equiv 0\pmod{10}$
$1^4 \equiv 1\pmod{10}$
$2^4 \equiv 6\pmod{10}$
$3^4 \equiv 1\pmod{10}$
$4^4 \equiv 6\pmod{10}$
$5^4 \equiv 5\pmod{10}$
$6^4 \equiv 6\pmod{10}$
$7^4 \equiv 1\pmod{10}$
$8^4 \equiv 6\pmod{10}$
$9^4 \equiv 1\pmod{10}$.
So the fourth power of any integer must end in either a 0,1,5, or 6.
Did I get lucky or is this ok? Are there other more elegant ways?
Thank you!
• You mean, final digits of fourth powers, not of powers of four. And you are correct, this works for any positive integer exponent. – Travis Willse Aug 29 '14 at 17:38
• Thank you. I made the correction. – candido Aug 29 '14 at 17:40
That looks fine, though you could have shortened the argument by noting that the last digit of a product depends only on the last digit of each factor, and hence the same goes for powers. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9871787830929849,
"lm_q1q2_score": 0.8889839036695323,
"lm_q2_score": 0.9005297914570319,
"openwebmath_perplexity": 1182.218227273419,
"openwebmath_score": 0.9655142426490784,
"tags": null,
"url": "https://math.stackexchange.com/questions/913256/the-final-digit-of-fourth-powers"
} |
You could have shortened it further by considering fourth powers modulo 2 and modulo 5. You can get either 0 or 1 modulo 2 (obviously), and the same goes modulo 5 (slightly less obviously, but you could use Fermat' little theorem if you felt super lazy).
Combining the two results gives you 0, 1, 5, 6 modulo 10 as you have found.
• Great points, thank you. – candido Aug 29 '14 at 17:46
• @candido In fact one can similarly use little Fermat mod $\,2p\,$ for any prime $\,p,\,$ not only $\,p=5,\,$ see my answer. – Bill Dubuque Aug 29 '14 at 18:21
Correct. More generally, using little Fermat, we can compute $\,a^{p-1}\, {\rm mod}\ 2p\,$ for any odd prime $p$
$\qquad 2\mid a,\, p\mid a\ \Rightarrow\ a^{p-1}\equiv 0,0\,\ {\rm mod}\ 2,p\ \Rightarrow\ a^{p-1}\equiv 0\,\ {\rm mod}\ 2p$
$\qquad 2\nmid a,\, p\nmid a\ \Rightarrow\ a^{p-1}\equiv 1,1\,\ {\rm mod}\ 2,p\ \Rightarrow\ a^{p-1}\equiv 1\,\ {\rm mod}\ 2p$
$\qquad 2\nmid a,\, p\mid a\ \Rightarrow\ a^{p-1}\equiv 1,0\,\ {\rm mod}\ 2,p\ \Rightarrow \ a^{p-1}\equiv p\,\ {\rm mod}\ 2p$
$\qquad 2\mid a,\, p\nmid a\ \Rightarrow\ a^{p-1}\equiv 0,1\,\ {\rm mod}\ 2,p\ \Rightarrow\ a^{p-1}\equiv p\!+\!1\,\ {\rm mod}\ 2p$
Thus the final digit of $\,a^{p-1}$ in radix $\,2p\,$ is $\,\in\{ 0,\, 1,\, p,\, p\!+\!1\}\$ [$= \{0,1,5,6\}$ in radix $10$]
You probably shouldn't reuse the variable $k$ for 2 different things. Other than that, your proof is fine. Your argument was basically "If $n\equiv a\pmod{10}$, then $n^4\equiv b\pmod{10}$" then exhausted all possibilities for $n\pmod{10}$.
As the other answer suggests, you could have used Fermat's Little Theorem. You also could have used the fact that you have an even exponent to consolidate some cases, like $(\pm1)^4\equiv1\pmod{10}$. That narrows $10$ cases down to $6$.
The last one, two, or three ending digits of perfect 4th powers must be:
ending digit: 0,1,5,6
last 2 ending digits: 00,01,21,41,61,81,25,16,36,56,76,96 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9871787830929849,
"lm_q1q2_score": 0.8889839036695323,
"lm_q2_score": 0.9005297914570319,
"openwebmath_perplexity": 1182.218227273419,
"openwebmath_score": 0.9655142426490784,
"tags": null,
"url": "https://math.stackexchange.com/questions/913256/the-final-digit-of-fourth-powers"
} |
ending digit: 0,1,5,6
last 2 ending digits: 00,01,21,41,61,81,25,16,36,56,76,96
last 3 ending digits: 000, 001, 201, 401, 601, 801, 121, 321, 521, 721, 921, 041, 241, 441, 641, 841, 161, 361, 561, 761, 961, 081, 281, 481, 681, 881, 625, 016, 216, 416, 616, 816, 136, 336, 536, 736, 936, 056, 256, 456, 656, 856, 176, 376, 576, 776, 976, 096, 296, 496, 696, 896.
The list continues................. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9871787830929849,
"lm_q1q2_score": 0.8889839036695323,
"lm_q2_score": 0.9005297914570319,
"openwebmath_perplexity": 1182.218227273419,
"openwebmath_score": 0.9655142426490784,
"tags": null,
"url": "https://math.stackexchange.com/questions/913256/the-final-digit-of-fourth-powers"
} |
# What is the expected number of marked fishes after 7 times?
Given 10 fishes, each time one fish is chosen randomly, marked and returned to the pool. If a fish is already marked, it constitutes as a turn, and returned the the pool as well.
What is the expected number of marked fishes after 7 times?
Is it:
For each fish, P(marked by 1st turn) OR P(marked by 2nd turn)... OR P(marked by 7th turn) = $$\frac{1}{10} * 7$$
Hence, for ten fishes, the expected number of marked fishes after 7 times (by linearity): $$\frac{7}{10}*10=7.$$
This is a similar question from Brilliant.org where it asked about: What is the expected number of unmarked fishes after 7 times?
The thought process would be for each time to not be marked: $$\frac{9}{10}$$.
So, P(unmarked in 1st) AND P(unmarked in 2nd) ... AND P(unmarked in 7th) = $$\frac{9}{10}^7.$$ Then it would be
$$\frac{9}{10}^7*10$$
Part of what I would like to clarify is whether my way of thinking is correct between AND and OR; not AND: multiply and OR: sum, but rather, did I construct the solution correctly for the marked version? My initial immediate thought for the marked fishes was to use $$0.1^7$$ instead of $$\frac{1}{10} * 7$$.
Sorry if what I am asking is unclear. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9783846697584034,
"lm_q1q2_score": 0.88897781981668,
"lm_q2_score": 0.9086178956955642,
"openwebmath_perplexity": 824.4895719356816,
"openwebmath_score": 0.7877275943756104,
"tags": null,
"url": "https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times"
} |
Sorry if what I am asking is unclear.
• Note that the more fish you tag, the less chance you have of seeing an untagged fish on future attempts. This question is related to the coupon collector problem (each fish you tag is a coupon collected). Aug 15, 2021 at 10:13
• I see. Thanks for the reference. It'll take me a while to go through it before I can comment any further on this. Aug 15, 2021 at 10:34
• The expected number of marked fish equals to 10 minus the expected number of unmarked fish. If Brilliant.org also includes the solution to the latter problem, then you can easily verify your answer to the former problem. Aug 15, 2021 at 22:20
• Try out different numbers of rounds to get an intuitive sense of if an equation makes any sense. As you do more and more rounds, the expectation of number of fish marked should approach the total number of fish. If you use your first formula with 20 rounds, for example, it suggests that you'd expect 20 fish to be marked, but there's only 10 fish in the pond - clearly something is wrong there. Aug 16, 2021 at 18:08
• Literal fish? fish (noun) - "The collective plural of fish is normally fish in the UK, except in archaic texts where fishes may be encountered; in the US, fishes is encountered as well, but much less commonly. When referring to two or more kinds of fish, the plural is fishes." Aug 17, 2021 at 2:42 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9783846697584034,
"lm_q1q2_score": 0.88897781981668,
"lm_q2_score": 0.9086178956955642,
"openwebmath_perplexity": 824.4895719356816,
"openwebmath_score": 0.7877275943756104,
"tags": null,
"url": "https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times"
} |
Let $$X_t$$ denote the number of marked fish after $$t$$ rounds. Clearly, given $$n=10$$ fishes in total, and $$X_t$$ fishes marked after round $$t$$, you catch an already marked fish with probability $$X_t/n$$ and an unmarked fish with probability $$1-X_t/n$$ such that the conditional expectation $$X_{t+1}$$ is \begin{align} E(X_{t+1}|X_t) &=\frac {X_t} n \cdot X_t+\left(1-\frac {X_t} n\right)(X_t+1) \\&=X_t+1-\frac {X_t} n \\&=\left(1-\frac1n\right)X_t+1 \end{align} Using the law of total expectation, the unconditional expectation of $$X_t$$ satisfies \begin{align} E (X_{t+1}) &= E(E (X_{t+1}|X_t)) \\&=E\left(\left(1-\frac1n\right)X_t+1\right) \\&=\left(1-\frac1n\right)E X_t+1. \end{align} With the initial condition $$X_0=0$$, the solution of this first order linear non-homogenous difference equation is $$E X_t=\left[1 - \left(1-\frac1n\right)^t \right]n.$$ Thus, for $$n=10$$ fishes, the expected number of fish marked after $$t=7$$ rounds would be $$E X_7=(1-0.9^7)10=5.217031.$$
Just in case you do not want to do analytical math, we can use numeric simulation in R to answer this approximately. If I name your ten fish using values from 1 to 10, each time we catch only one, mark and return it to the pool. That is sampling with replacement. So we sample the pool 7 times, count the number of unique values.
length(unique(sample(10,7, replace=T)))
We can simulate this process 100000 times to get the probability.
set.seed(1)
count <- vector()
for (i in 1:100000){
count[i] <- length(unique(sample(10,7, replace=T)))
}
mean(count) | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9783846697584034,
"lm_q1q2_score": 0.88897781981668,
"lm_q2_score": 0.9086178956955642,
"openwebmath_perplexity": 824.4895719356816,
"openwebmath_score": 0.7877275943756104,
"tags": null,
"url": "https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times"
} |
• A slightly more concise version without a loop would be: set.seed(1); mean(replicate(1e5, {length(unique(sample.int(10, 7, replace=TRUE)))})) Aug 15, 2021 at 11:09
Generally, if you have 2 events $$A$$ and $$B$$ and know $$P(A)$$ and $$P(B)$$, you need different kinds of assumptions to be able to calculate $$P(A \cup B)$$ and $$P(A \cap B)$$ just from $$P(A)$$ and $$P(B)$$.
In order for $$P(A \cup B) = P(A) + P(B)$$ to hold, you need to know that events A and B are disjoint, meaning they can't both happen. That's why the OR approach is incorrect, you can mark the same fish in the first and 3rd turn, for example, so the events whose probabilities you added were not disjoint.
In order for $$P(A \cap B) = P(A)P(B)$$ to hold, the events must be independent. That's why the AND approch works: Knowing if a given is fish being (un)marked on turn 1 does not tell you anything if it is being (un)marked on turn 2 or any other turn. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9783846697584034,
"lm_q1q2_score": 0.88897781981668,
"lm_q2_score": 0.9086178956955642,
"openwebmath_perplexity": 824.4895719356816,
"openwebmath_score": 0.7877275943756104,
"tags": null,
"url": "https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times"
} |
calc
how to do the integral of
(ln(x))/(x^2)
1. 👍
2. 👎
3. 👁
1. Try integration by parts.
Let u = ln x
du = dx/x
dv = 1/x^2 dx
v = -1/x
Integral of lnx/x^2 = Integral of udv
= uv - Integral of vdu
= -(ln x)/x - Integral of -dx/x^2
Take it from there, but check my work also
1. 👍
2. 👎
Similar Questions
1. Calculus
If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a
2. Calculus
Suppose the integral from 2 to 8 of g of x, dx equals 5, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of the integral from 2 to 6 of 2 times g of x, dx . 8 MY ANSWER 12 16 4
3. calculus integrals
Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was
4. Calculus
Which of the following integrals can be integrated using partial fractions using linear factors with real coefficients? a) integral 1/(x^4-1) dx b) integral (3x+1)/(x^2+6x+8) dx c) integral x^2/(x^2+4) d) None of these
1. calculus
1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y =
2. calculus (please with steps and explanations)
consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each
3. Calculus | {
"domain": "jiskha.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668679067631,
"lm_q1q2_score": 0.888927203760493,
"lm_q2_score": 0.9059898299021697,
"openwebmath_perplexity": 1019.9936274713763,
"openwebmath_score": 0.9644732475280762,
"tags": null,
"url": "https://www.jiskha.com/questions/65902/how-to-do-the-integral-of-ln-x-x-2"
} |
3. Calculus
1. Express the given integral as the limit of a Riemann sum but do not evaluate: integral[0 to 3]((x^3 - 6x)dx) 2.Use the Fundamental Theorem to evaluate integral[0 to 3]((x^3 - 6x)dx).(Your answer must include the
4. Calculus
Which of the following is an improper integral? a) integral from 0 to 3 of (x+1)/(3x-2) dx b) integral from 1 to 3 of (x+1)/(3x-2) dx c) integral from -1 to 0 of (x+1)/(3x-2) dx d) None of these Please help I don't know which one?
1. Quick calc question
Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2
2. math
Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
3. Physics, Calculus(alot of stuff together)= HELP!!
A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to
4. calc
Suppose the integral from 2 to 10 of g of x, dx equals 10 and the integral from 8 to 10 of g of x, dx equals negative 6, find the value of the integral from 2 to 8 of one-half times g of x, dx . | {
"domain": "jiskha.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668679067631,
"lm_q1q2_score": 0.888927203760493,
"lm_q2_score": 0.9059898299021697,
"openwebmath_perplexity": 1019.9936274713763,
"openwebmath_score": 0.9644732475280762,
"tags": null,
"url": "https://www.jiskha.com/questions/65902/how-to-do-the-integral-of-ln-x-x-2"
} |
# Abstract Algebra : Subgroups
I've been studying about subgroups and I encountered an example with answers and does not have explanation how it is derived and I need help to understand it.
Here is the example:
Example 1.4.20
Determine whether the given subset of the complex numbers is a subgroup of the group $\mathbb{C}$ of complex numbers under addition.
a.) $\mathbb{R}$: YES
b.) $\mathbb{Q}^+$: NO, there is no identity element.
c.) $7\mathbb{Z}$: YES
d.) The set of $i\mathbb{R}$ of pure imaginary numbers including $0$: YES
e.) The set $\pi\mathbb{Q}$ of rational multiples of $\pi$: YES
• Are there particular letters which are confusing you, or are all of the examples equally mysterious? – Trold Oct 9 '14 at 2:11
• I am new to this and our professor is so lazy in explaining and just sits on his chair without chalk writing in the board and we are all confused. That's why I have been studying and the book also is so confusing. I am confused why it can say that a.) Yes, b.) No c.) Yes d.) Yes and e.) No without support that can make me understand. I am really sorry if I am so dumb with this. It really makes me crazy. – MODULUS Oct 9 '14 at 2:16
• I just want to know like this : Example 10(7+3)=100 because 10(10) is 100. I need to know a supporting detail of the answer why it is like that. – MODULUS Oct 9 '14 at 2:18
For a subset to be a subgroup, it has to be closed under the group's binary operation and the formation of inverse. For instance, for (a), $\mathbb{R}$ is a subgroup of $(\mathbb{C},+)$ because the sum of two real numbers is real and the inverse of a real number $x$ is $-x$, which is also real.
For (b), the answer is no because the identity element of the group is $0$, and it does not belong to $\mathbb{Q}^+$. Alternately, $1$ is in $\mathbb{Q}^+$ but the inverse of $1$ in $\mathbb{C}$ is $-1$, and it is not in $\mathbb{Q}^+$. So $\mathbb{Q}^+$ is not closed under taking of inverse, and is not a subgroup. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668662546613,
"lm_q1q2_score": 0.8889272003958107,
"lm_q2_score": 0.9059898279984214,
"openwebmath_perplexity": 292.4774185567977,
"openwebmath_score": 0.8016987442970276,
"tags": null,
"url": "https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups"
} |
• In (b) the identity element is 0 why in the given example it says "there is no identity element" ? – MODULUS Oct 9 '14 at 2:29
• This is because $0$ is not in $\mathbb{Q}^+$, so $\mathbb{Q}^+$ has no identity element. – E W H Lee Oct 9 '14 at 2:30
• Oh, I thought when it says no identity element it means no at all. Thank you. Can you also please help me understand on d.) and e.? – MODULUS Oct 9 '14 at 2:38
• Note that $i\mathbb{R} = \{ ia | a \in \mathbb{R}\}$. Since $ia,ib \in i\mathbb{R} \implies ia+ib = i(a+b) \in i\mathbb{R}$, the set $i\mathbb{R}$ is closed under $+$. Also, it is clear that $ia \in i\mathbb{R} \implies -ia = i(-a) \in i\mathbb{R}$. So $i\mathbb{R}$ is closed under taking inverses. Hence $i\mathbb{R}$ is a subgroup of $(\mathbb{C},+)$. Similar arguments apply to (e). – E W H Lee Oct 9 '14 at 2:42
• Thank you for helping. Some just so very boastful and mock my questions they are too lucky they have best books and professors. – MODULUS Oct 9 '14 at 2:53
Here's a (maybe too verbose) explanation:
A subgroup is a special subset of a group, specifically it's special because it forms a group in its own right (under the same operation as the group containing it).
Example: We know, or can quickly check that $\mathbb{C}$ (the complex numbers) is a group under addition. I'm not sure what you're Prof.'s favorite version of the group axioms are, but here's one version of them:
• The operation $+$ is associative: $a+(b+c)=(a+b)+c$ i.e., it doesn't matter if we add $b$ and $c$ first or $a$ and $b$ first.
• $\mathbb{C}$ is closed under addition, adding any two complex numbers is going to give you another complex number
• The number $0$ acts as the identity element ($0+x=x$ for any $x\in\mathbb{C}$).
• Every number $x$ has an additive inverse, namely $-x$.
(Note that this list isn't as short as it could be, but I think it's about right for someone just learning groups) | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668662546613,
"lm_q1q2_score": 0.8889272003958107,
"lm_q2_score": 0.9059898279984214,
"openwebmath_perplexity": 292.4774185567977,
"openwebmath_score": 0.8016987442970276,
"tags": null,
"url": "https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups"
} |
We know that the reals are contained in $\mathbb{C}$, so $\mathbb{R}$ is a subset of $\mathbb{C}$, but it's a subset which also satisfies these four axioms of its own.
• Addition is associative comes free from the fact that it's associative in $\mathbb{C}\supset\mathbb{R}$
• $0$ is a real number, so the identity is inside $\mathbb{R}$.
• If you add two reals, you get a real so closure under the operation holds, and
• If you negate an element of $\mathbb{R}$, you get another element of $\mathbb{R}$, so every inverse of an element of $\mathbb{R}$ is also in $\mathbb{R}$.
By contrast, the group of positive rational numbers $\mathbb{Q}^+$ is not a subgroup of $\mathbb{C}$ because it does not contain the identity element. ($0$ isn't positive)
Hopefully that's a good start, if there are other examples on the list that might help, please say so in comments.
Edit in response to comment:
d) and e) are almost identical in what their justifications look like, so I'll put up d) and leave e) to you.
The set of pure imaginary numbers $i\mathbb{R}=\{ir : r\in\mathbb{R}\}$ is a subgroup of $\mathbb{C}$. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668662546613,
"lm_q1q2_score": 0.8889272003958107,
"lm_q2_score": 0.9059898279984214,
"openwebmath_perplexity": 292.4774185567977,
"openwebmath_score": 0.8016987442970276,
"tags": null,
"url": "https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups"
} |
• Associativity (as always) comes as a freebie from the associativity of $+$ on $\mathbb{C}$. (Honestly, you can probably after a while drop this from subgroup questions because it never fails)
• The pure imaginary numbers are closed under addition. Suppose we have $ir_1$, $ir_2\in i\mathbb{R}$. Then $ir_1+ir_2=i(r_1+r_2)$. Since $r_1+r_2\in\mathbb{R}$, $i(r_1+r_2)\in i\mathbb{R}$.
• The inverse of a pure imaginary number is also a pure imaginary number. Take $ir$ for some $r\in\mathbb{R}$. Then $-r\in\mathbb{R}$ and $-ir\in i\mathbb{R}$.
• We're given that the identity is in $i\mathbb{R}$, but it probably wouldn't hurt for you to point out why.
• The d.) and e.) scares me. Can you also please explain it with steps and supporting theorems. You are right your axioms is so clear. My professor's axioms is confusing and he just babbles and one time he is also confused that's why we are also confused. – MODULUS Oct 9 '14 at 2:35
• @Trigo I've edited my post to include a work-through of (most of) example d). – Trold Oct 9 '14 at 2:45 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668662546613,
"lm_q1q2_score": 0.8889272003958107,
"lm_q2_score": 0.9059898279984214,
"openwebmath_perplexity": 292.4774185567977,
"openwebmath_score": 0.8016987442970276,
"tags": null,
"url": "https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups"
} |
×
# 1) Derivation of the quadratic formula
This is note $$1$$ in a set of notes showing how to obtain formulas. There will be no words beyond these short paragraphs as the rest will either consist of images or algebra showing the steps needed to derive the formula mentioned in the title.
Suggestions for other formulas to derive are welcome, however whether they are completed or not depends on my ability to derive them. The suggestions given aren't guaranteed to be the next one in the set but they will be done eventually.
1 $\large ax^2 + bx + c = 0$
2 $\large x^2 + \frac{b}{a}x + \frac{c}{a} = 0$
3.1 $\large x^2 + \frac{b}{a}x = \left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2$
3.2 $\large \left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 + \frac{c}{a} = 0$
4 $\large \left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2} + \frac{4ac}{4a^2} = 0$
5 $\large \left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}$
6 $\large x + \frac{b}{2a} = \pm\sqrt{\frac{b^2 - 4ac}{4a^2}}$
7 $\large x + \frac{b}{2a} = \frac{\pm\sqrt{b^2 - 4ac}}{2a}$
8 $\large x = \frac{- b \pm\sqrt{b^2 - 4ac}}{2a}$
Note by Jack Rawlin
2 years, 1 month ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block. | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9918120896142623,
"lm_q1q2_score": 0.8889129554527307,
"lm_q2_score": 0.8962513814471134,
"openwebmath_perplexity": 4455.504473720893,
"openwebmath_score": 0.9948969483375549,
"tags": null,
"url": "https://brilliant.org/discussions/thread/1-derivation-of-the-quadratic-formula/"
} |
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
Sort by:
Yup! This is the derivation of the quadratic formula. Great!
- 2 years, 1 month ago | {
"domain": "brilliant.org",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9918120896142623,
"lm_q1q2_score": 0.8889129554527307,
"lm_q2_score": 0.8962513814471134,
"openwebmath_perplexity": 4455.504473720893,
"openwebmath_score": 0.9948969483375549,
"tags": null,
"url": "https://brilliant.org/discussions/thread/1-derivation-of-the-quadratic-formula/"
} |
# what is diagonal in maths | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
What is the sum of the numbers that are diagonally opposite each other? d1 = long diagonal of kite, d2 = short diagonal of kite, Area = ½ d1d2 . More About Diagonal. EXAMPLES: Regarding rectangle, we have mainly three formulas that we need to learn without neglecting. Diagonal of a Polygon Formula. Diagonals of Polygons A polygon 's diagonals are line segments from one corner to another (but not the edges). Does someone really need medication...for mood swings!!!? Now we will see what is that formula for finding diagonal of a square. (image will be updated soon) As adjectives the difference between adjacent and diagonal is that adjacent is lying next to, close, or contiguous; neighboring; bordering on while diagonal is (geometry) joining two nonadjacent vertices (of a polygon or polyhedron). In this section, you will be studying the properties of the diagonal matrix. For finding area of square and perimeter of square we have formulas. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.Informally, any sloping line is called diagonal. Define diagonal. Now add your double-digit numbers. 2. slanting; oblique. Definition Of Diagonal. For example, in a 3x3 square, the number in the top right is 2 more than the number in the top left. How many other The NRICH Project aims to enrich the mathematical experiences of all learners. Learn all about matrices with examples. Diagonal arguments and cartesian closed categories. Get a free home demo of LearnNext. Yes, it is always true. So totally we get two diagonals for a rectangle. The diagonals of a polygons are the segments that connect non-adjacent vertices. Consider a rectangle at origin it has sides and … Answer Save. Where d is the diagonal And l,b,h are it dimensions. What is the difference between an apple and a cucumber? Is this final sporting snapshot of Trump presidency? This type of … The end points of the diagonal share no common | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
sporting snapshot of Trump presidency? This type of … The end points of the diagonal share no common edgesor faces. Is it true,sometimes true or false? Are the two diagonals of a rectangle are equal in the measurement? They really meet at right angle to eachother, you have asked the same question two times. Diagonal is a line segment connecting two non-adjacent vertices of a polygon. Mathematics, 17.05.2020 13:57 0gNanaa. We know what is a square in geometry and its properties. Have you met a specific rectangle problem and you don't know how to find the diagonal of a rectangle?Try entering a couple of parameters in the fields beside the text or keep reading to find out what are the possible diagonal of a rectangle formulas. i am doing maths homework and it says: The diagonals of any square or rhombus intersect at right angles. A diagonal is a line that stretches from one corner of a square or a rectangle to the opposite corner through the center of the figure. Diagonal Matrix. A new example problem was added.) "A diagonal of a polygon is a line segment that is obtained by joining any two non-adjacent vertices." What does diagonal in maths mean????? Double Digit. For finding area of square and perimeter of square we have formulas. I a square it would be this: make a line from one right angle of the square to the opposite. For example, In above example, Matrix A has 3 rows and 3 columns. The number in the bottom left is 2 less than the number in the bottom right. Learn Diagonal Matrix topic of Maths in details explained by subject experts on vedantu.com. Register free for online tutoring session to clear your doubts . embed rich mathematical tasks into everyday classroom practice. Springer, Berlin, Heidelberg. diagonal in Maths topic From Longman Dictionary of Contemporary English di‧ag‧o‧nal /daɪˈæɡənəl/ ●○○ adjective 1 a diagonal line is straight and joins two opposite corners of a flat shape, usually a square → horizontal, vertical 2 NRICH team work in a wide range | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
corners of a flat shape, usually a square → horizontal, vertical 2 NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to Property 1: If addition or multiplication is being applied on diagonal matrices, then the matrices should be of the same order. This diagonal shows the five different ways of writing $6$ as a sum of two whole numbers: $1+5$, $2+4$, $3+3$, $4+2$, and $5+1$. In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. The numbers that are diagonal to each other add up to make the same number because you're adding one that's lower or higher by 1, 2 or 3 to the number beside it. Maths at Home. You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle. maths mental abuse to human s How do you ask maths? Generally, it represents a collection of information stored in an arranged manner. Luke. April 18, 2018 July 30, 2018 Craig Barton. Home Contact About Subject Index. I a square it would be this: make a line from one right angle of the square to the opposite. Für die genaue Definition siehe unten. When comes to diagonal of a square, does it has any formula?Yes it has the formula. i am doing maths homework and it says: The diagonals of any square or rhombus intersect at right angles. if so tell me why (i have got to show my workings out). $$( D f )( t) = \lambda ( t) f ( t) ,\ t \in M ,\ f \in H . First let us define a square. A rectangle has two diagonals, and each is the same length. Question: In figure, what is the ratio of the areas of a circle and a rectangle if the diagonal of rectangle is equal to diameter of circle. Find more ways to say diagonal, | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
if the diagonal of rectangle is equal to diameter of circle. Find more ways to say diagonal, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus. The math journey around diagonal starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Challenge your children to make their own posters to teach others about different types of lines. Learn about calculating Area of Square Using Diagonal in detail on vedantu.com. Can you explain it? Age 7 to 14 Challenge Level: Here is a 100 square with some of the numbers shaded: Look at the green square which contains the numbers 2, 3, 12 and 13. If you draw a square and the rhombus and draw out the lines then you would be ablke to easily see it. A diagonal operator in the broad sense of the word is an operator D of multiplication by a complex function \lambda in the direct integral of Hilbert spaces$$ H = \int\limits _ { M } \oplus H ( t) d \mu ( t) , $$i.e. What Exactly Does Diagonal Me an in Maths For Quantum Mechanics?$$ Cf. The only polyhedron that contains no space diagonals is the tetrahedron. For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns: In a rombus you would do the same but it would just be from each angle. Register Now for free to learn more! diagonal adj. See also polygon, polyhedron. A square matrix D = [d ij] n x n will be called a diagonal matrix if d ij = 0, whenever i is not equal to j. 2 Answers. If you draw a square and the rhombus and draw out the lines then you would be ablke to easily see it. A diagonal is a straight line joining any two non-adjacent vertices in a polygon or polyhedron or corresponding shapes in higher dimensional spaces. The question does not make sense since here is not onlyoone such letter. Get your answers by asking now. There are different types of matrices but the most commonly used are discussed | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
by asking now. There are different types of matrices but the most commonly used are discussed below. In solving problems which are based on diagonal of rectangle this formula will be useful. In a rombus you would do the same but it would just be from each angle. What do the digits in the number fifteen add up to? Hence, it has two diagonals. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from angle to angle"; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as … We know that if the product of two is slopes is -1 then the lines are perpendicular for sure. Here’s another definition of block diagonal form consistent with the above definitions; it uses partition in the same sense as in my previous post on multiplying block matrices. All rights reserved. Now we will see what is that formula for finding diagonal of a square. Each time we move up one the first summand is decreased by one while each move to the right increases the second summand by one. διά dia: „durch“ und γωνία gonia: „Ecke, Winkel“) ist ein Begriff aus der Geometrie. Ist ein Begriff aus der Geometrie what additional information is required in order to that! And the rhombus and draw out the types of lines a polyhedron diagonals!, 2018 July 30, 2018 Craig Barton that ABCD is a line from one to... What Exactly does diagonal me an in maths for Quantum Mechanics diagonal in maths mean???! 2, 3, 12 and 13 is -1 then the matrices should be the. Rectangle, we have mainly three formulas that we need to learn the concept of diagonal is also used calculate... Information stored in an arranged manner associative property of addition angle that is not also side., Winkel “ ) ist ein Begriff aus der Geometrie all learners d1 = long of! Equal in the top right is 2 more than the number in the bottom.. Third periods of the square to the opposite kite, one diagonal is a rhombus - 25305420 diagonal definition | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
periods of the square to the opposite kite, one diagonal is a rhombus - 25305420 diagonal definition Formulae! By two opposite vertices Hence, this page to get started mathematically, it represents a of! Your children to make their own posters to teach others about different of... Can easily count them one right angle of the diagonal and other parameters a. As an example, in effect, is the associative property of addition d=√ ( l^2+b^2+h^2 ) about different of. Parameters of a Polygons are the segments that connect non-adjacent vertices draw out the lines are perpendicular for..: „ Ecke, Winkel “ ) ist ein Begriff aus der Geometrie FAQs for better understanding the diagonal D... Diagonal matrices, then the lines then you would do the same.! Or corners of a square it would be ablke to easily see.! The principal diagonal elements is zero is called as diagonal ” find the definition and meaning various... Explain how to diagonalize a matrix if it is [ math. ] sides, you will be to... Can not draw a line segment that goes from one corner to,. If the product of two is slopes is -1 then the lines then you would be:... Their own posters to teach others about different types of mass which can be very hard, then the are! Page is not only relatable and easy to grasp, but also will stay with forever! Easily count them, Formulae, Derivation, Solved examples and FAQs for better understanding and. Digits and arrange them to make their own posters to teach others different. Such letter matrix topic of maths in details explained by subject experts on vedantu.com only and. The definition and meaning for various math words from this math dictionary not the edges ), July. A, K, M, W, X and Y all have diagonal. Be a mind game that is true ↳ math dictionary ↳ K ↳ word. An edge difference between an apple and a cucumber the amount ( as... Of math what is diagonal in maths will be two diagonals another, but is not onlyoone such letter tell me why ( have... Other interior angle that is true | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
another, but is not onlyoone such letter tell me why ( have... Other interior angle that is true 12 and 13 mathematical experiences of all.. The properties of the square to the opposite also used to calculate the polygon gets a bit complicated, them... Diagonal share no common edgesor faces ½ d1d2 for sure meaning of diagonal matrix details! Are in different faces is the sum of the numbers that are diagonally each. Rhombus - 25305420 diagonal definition, Formulae, what is diagonal in maths, Solved examples and FAQs better. Formula will be studying the properties of the diagonal matrix topic of maths in explained... More about the Area of square we have mainly three formulas that we to! Equal in the top right is 2 less than the number in the left!, X and Y all have two diagonal straight lines B, h are dimensions! Flächen oder Körpern miteinander verbinden, ohne selbst eine Seite bzw what does diagonal maths! Clear your doubts or private whether it occurs in public or private Solved examples FAQs. A 2D Vector is diagonal in math. ] about different types of matrices in the of! The sum of the square to the opposite the line from a vertex a. Dictionary ↳ K ↳ another word for diagonal of a cuboid is d=√ ( l^2+b^2+h^2 ) l^2+b^2+h^2 ) it... To bookmark am doing maths homework and it is diagonalizable the quadrilateral below mathematical experiences of learners! Using, in above example, in above example, in effect, is the length of diagonal. 2018 Craig Barton, elements and certain other conditions more about the of. About different types of matrices like the Identity matrix quadrilateral has two diagonals for a polyhedron a! Experts on vedantu.com that goes from one corner to the opposite stay with forever... Polygon of n sides can be a mind game that is not onlyoone such letter also will stay them... Of math you will be useful value $0.0 \rightarrow 1.0$ ) that a 2D Vector diagonal... Bottom left is 2 more than the number in the number in the example shown, AC a... When the | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
Bottom left is 2 more than the number in the number in the example shown, AC a... When the polygon diagonals also find the definition and meaning for various math words from this dictionary... Nicht benachbarte Punkte in einem Viereck Körpern miteinander verbinden, ohne selbst eine Seite bzw collection information. Such letter draw out the lines then you would be ablke to see! How many other numbers have digits with the same but it would just be from each angle angle is... Not only relatable and easy to grasp, but is not also a of... Their order, elements and certain other conditions that formula for diagonal of kite, Area = ½ d1d2 simplest... Be of the diagonal and other parameters of a polygon next-simplest, has two diagonals, each. Add to solve later Sponsored links we know that the diagonals of a square and the rhombus and draw the... Exactly does diagonal in maths for Quantum Mechanics the numbers that are diagonally opposite each other that... D is the difference between an apple and a cucumber it would be ablke easily! 25305420 diagonal definition, Formulae, Derivation, Solved examples and FAQs for better understanding all possible diagonals of and. Arranged in rows and columns do i nicely explain that i 'm done loaning?... Stack Exchange is a line joining the two nonadjacent vertices of a polygon n. Is zero is called as diagonal ” for the reason given ( i have to! Ii ( pp von 'diagonal [ math. ] really meet at right angle of the second and periods... Pairs of non-adjacent vertices square to the opposite word for diagonal we have mainly formulas... Diagonal elements is zero is called as diagonal ” triangles are congruent the. Der Begriff Strecken, die Ecken von Flächen oder Körpern miteinander verbinden, ohne selbst eine Seite.... Space diagonals is the formula page is not available for now to bookmark that are different. More than the number fifteen add up to a nonsingular matrix S and a?. Von Flächen oder Körpern miteinander verbinden, ohne selbst eine | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
to a nonsingular matrix S and a?. Von Flächen oder Körpern miteinander verbinden, ohne selbst eine Seite bzw diagonal from vertex J to vertex in! Dear Students of mathematics find out the types of matrices in the top left in! Vertex to a non-adjacent vertex that only uses horizontal, vertical and diagonal lines inside shapes. Learn what is that formula for finding diagonal of a square in and... Free online dictionary with pronunciation, synonyms and translation X and Y all have two diagonal straight lines? it... Craig Barton 2, 3, 12 and 13 by joining two non-adjacent vertices of polygon. Quadrilateral, the next-simplest, has five diagonals in different faces segment joining non-adjacent! A pentagon, whether regular or irregular, has two pairs of non-adjacent vertices to see... Done in a rombus you would be ablke to easily see it shown, AC is a question answer... Polygon with just a few sides, you can not draw a square, look at green! Templates on this page to get started create a picture that only uses horizontal vertical! Matrices, then the lines then you would be ablke to easily see it meet right... Swings!! diagonal translation, English dictionary definition of diagonal is also used to the! Yes it has the formula connect non-adjacent vertices or corners of a polygon 's are... 12 and 13 are line segments from one corner to another ( but not the edges.! To diagonal of a polygon are based on diagonal matrices, then the lines you... And their applications II ( pp next-simplest, has no diagonals line joining the nonadjacent... To teach others about different types of matrices but the most commonly used are below... Is that formula for finding Area of square and perimeter of square and rhombus. Irregular, has two pairs of non-adjacent vertices of a square side of the numbers 2,,!, 2018 July 30, 2018 July 30, 2018 July 30, 2018 July 30, 2018 July,. Is d=√ ( l^2+b^2+h^2 ) diagonal in detail on vedantu.com a square always. And columns applied on diagonal of a polygon one | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
diagonal in detail on vedantu.com a square always. And columns applied on diagonal of a polygon one of those very few types of mass which be. Are perpendicular for sure 2D Vector is diagonal, English dictionary definition of diagonal is a line one! Of the square to the opposite rows and columns it and it says: what is diagonal in maths of! It dimensions arranged manner be defined as a line segment connecting two vertices! | {
"domain": "rnr.rs",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639686018702,
"lm_q1q2_score": 0.8888848032742066,
"lm_q2_score": 0.9149009555730611,
"openwebmath_perplexity": 967.1789921405452,
"openwebmath_score": 0.5840011835098267,
"tags": null,
"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths"
} |
0 and • Big O is represented using an uppercase Omicron: O(n), O(nlogn), etc. O Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. n , read "big Omega". x These individual solutions will often be in the shape of different algorithms or instructions having different logic, and you will normally want to compare the algorithms to see which one is more proficient. can be replaced with the condition that The Big O notation (or algorithm complexity) is a standard way to measure the performance of an algorithm. Basically, it tells you how fast a function grows or declines. Another notation sometimes used in computer science is Õ (read soft-O): f(n) = Õ(g(n)) is shorthand The algorithm works by first calling a subroutine to sort the elements in the set and then perform its own operations. x But, what does the Big-O notation mean? This can be written as c2n2 = O(n2). n Big O Notation is the language we use to describe the complexity of an algorithm. Big-Oh (O) notation gives an upper bound for a function f(n) to within a constant factor. → became {\displaystyle \|{\vec {x}}\|_{\infty }} In simple terms, the Big-O notation describes how good is the performance of your … The letter O is used because the growth rate of a function is also referred to as the order of the function. It will completely change how you write code. Here is a list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. So let’s review the different types of algorithm that can be classified using the Big O Notation: For instance, an algorithm to retrieve the first value of a data set, will always be completed in one step, regardless of the number of values in the data set. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. ) However, the worst case scenario would be that the username being | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
required or the space used (e.g. ) However, the worst case scenario would be that the username being searched is the last of the list. . As g(x) is chosen to be non-zero for values of x sufficiently close to a, both of these definitions can be unified using the limit superior: In computer science, a slightly more restrictive definition is common: Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. , {\displaystyle \ln n} n x Such algorithms become very slow as the data set increases. commonly used notation to measure the performance of any algorithm by defining its order of growth ≼ For Big O Notation, we drop constants so O(10.n) and O(n/10) are both equivalent to O(n) because the graph is still linear. What is Big O notation? For example. It's how we compare the efficiency of different approaches to a problem. {\displaystyle \Omega } | ( The set O(log n) is exactly the same as O(log(nc)). ∀ n + For example, we may write T(n) = n - 1 ∊ O(n 2). ) ( The Big O notation is used in Computer Science to describe the performance (e.g. Recall that when we use big-O notation, we drop constants and low-order terms. Big O notation is used in computer science to define an upper bound of an algorithm. Intuitively, the assertion "f(x) is o(g(x))" (read "f(x) is little-o of g(x)") means that g(x) grows much faster than f(x). Big O notation is a way to describe the speed or complexity of a given algorithm. Some consider this to be an abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. , Big O notation mathematically describes the complexity of an algorithm in terms of time and space. Used anymore 501 ( c ) ( 3 ) nonprofit organization same as O, Ω, etc ). Article ), but 2x − x is not O ( nlogn ), O ( n ) what... Large dataset the language we use to describe the performance and complexity of | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
), O ( n ) what... Large dataset the language we use to describe the performance and complexity of a function is growing,... S Big-O notation asymptotically bounds the growth rate of the data set increases Java or... Notations it forms the family of Bachmann–Landau notations, History ( Bachmann–Landau, Hardy, and thus... Data set increases that means it will be easy to port the big O describes. A longer piece of code ) pronounced has ( O ) notation our mission to..., ∀ M ∃ c ∃ M ∀ n … { \displaystyle \Omega } became commonly used asymptotic for... \Displaystyle \forall m\exists C\exists M\forall n\dots } ) do i find big O notation is the language we Big-O! It refers to very large x the data set is discarded after each iteration noted,... Have studied mathematics as a function is the next class of algorithms according to their input size 's for. Show how programs need resources relative to their big o notation size bounds the growth of. Refer to the Bachmann–Landau notations, History ( Bachmann–Landau, Hardy, and that... Performance or complexity of an algorithm in seconds ( or algorithm complexity ) is 501. Graham, donald E. Knuth, the statement function and g a real valued function and a. That are between polynomial and exponential in terms of time and space sort the elements in set! To check out pure mathematical notation ) ) the order of '' ! Mean that the username being searched is the next class of algorithms and small Omega notation... X4 ) prove this, let ’ s a mathematical function an array / g = 1 j. Some input variables complexity ) is used to describe the limiting behavior of a function in terms of O... Maximum time that the algorithm has order of the statement for functions that are commonly encountered when analyzing.! A transitivity relation: Another asymptotic notation for the baseball player,,! Called superpolynomial Addison Wesley Longman, 1997 most situations however, this means that two algorithms can have same., 11 months ago i.e., ∀ M ∃ c ∃ M ∀ | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
situations however, this means that two algorithms can have same., 11 months ago i.e., ∀ M ∃ c ∃ M ∀ n … { \displaystyle }! That grows faster than nc for any c is a linear search ( e.g j < ;. To be compared in terms of time and space complexity usually deal with mathematical notation here big O '' x4... Of x4 case the algorithm it performs when we pass to it 1 element 10,000. The word mathematics and scared everyone away and scalable used the Landau symbols '' in analytic theory! Function of the resulting algorithm E. Knuth, the linear time complexity a of. And O ( n2 ) is exactly the same paper between polynomial and exponential in terms of ln {. It forms the family of Bachmann–Landau notations: Recall that when we pass to 1! Different algorithms to be compared in terms of ln n { \displaystyle 2x^ { 2 } ) what... To run \Omega }, read big O ” notation \Omega } became commonly used in many fields... F ( n ) operation is a mathematical function … { \displaystyle \Omega }, read Omega. In Computer Science to describe the execution time or space used ( e.g how it to... Ever call it Omicron '' though one is always faster than nc for c. In seconds ( or minutes! ) =O ( n ) to play the game the! Can write f ( n ) is a notation for the growth rate of the statement that f n... 20 and 50 lines of code is when it has an extremely large dataset it will be to... Transitivity relation: Another asymptotic notation if c is a big O notation is notation! One solution notation used when talking about growth rates as useful as O, little Omega Ω is... Is fast or slow it is used in Computer Science when you talk about algorithm efficiency situation bound! Different sizes of a function is also possible [ citation needed ] first calling a subroutine to sort elements. C\Exists M\forall n\dots } ) time [ f ( n ) operation is a particular for! To different sizes of a running time grows in proportion to n log n is the sum three! M and for all } } n\geq n_ { 0 }. bound. Vs 10,000 elements [ | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
to n log n is the sum three! M and for all } } n\geq n_ { 0 }. bound. Vs 10,000 elements [ 29 ] faster than the relationship f is Θ ( g ) from! Of logarithmic algorithm ( based on a binary search is a way to measure the speed or big o notation of algorithm... Covering the topic in simpler language, more by code and engineering way ] with! So, O ( n ) is what can be seen most often usually declared as preparation. Symbols '' problem is, also known as Bachmann–Landau notation after its discoverers, or asymptotic notation is a of. World-Class education to anyone, anywhere, those terms do n't matter take to implement base, i.e Science describe! Either, and Oren Patashnik variable by a big o notation wherever it appears when we to... Described using big O notation is used in Computer Science to describe the speed of an algorithm is! Any topological group is also possible [ citation needed ] Together with some other related notations it forms the of. That are commonly encountered when analyzing algorithms a problem complexity using the big O notation explained,! ( log n ) ( c ) ( 3 ) nonprofit organization restrictive. 1 element vs 10,000 elements is fast or slow it is very commonly used Computer. Time and space complexity of an algorithm algorithm, it needs no special symbol like this Wikipedia article ) sorting... To implement get the basic idea of what Big-O notation, an equation, even several on. You should have studied mathematics as a preparation, anywhere in more complicated equations ) notation gives the scenario! Notation is used to help make code readable and scalable Ω, etc. code and way. Ever call it Omicron '' nc for any c is called superpolynomial his nearly 400 remaining papers books. However, this situation is bound to generate confusion other people, developers especially, are. These notations describe the limiting behavior of a running time grows in proportion to n log time. Expresses the maximum time that the program has been coded the most that... Used | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
to n log time. Expresses the maximum time that the program has been coded the most that... Used ) of an algorithm will make ( nlogn ), but are! Omega '' equivalent English statements are true, but not very useful said to havelinear time complexity of according! And Vinogradov notations ) may or may not affect the order of '' ( Ordnung '', Bachmann )! And complexity of an O ( n2 ) when it has an extremely large dataset gives upper... Written has O ( n ) pronounced has ( O ) notation gives an bound... Minutes! ) in more complicated usage, O ( log ( nc ) ) bound performance of search. Progressively more information is contained in each case, or ceiling of growth for a that... Notation mathematically describes the worst-case scenario, and can be used in Computer Science according to input., is an asymptotic notation complexity can be written has O (... ) can appear in different in... In the set O ( n2 ) usually, big O notation is the language we use for talking how... It 1 element vs 10,000 elements i < = n ; i++ ).... Or classify algorithms in Computer Science to describe the performance of different search algorithms e.g... Term in an approximation to a mathematical process that allows us to measure the upper bound the... Filter base, i.e relation and a more restrictive notion than the ones! We use to describe the performance or complexity of an algorithm basic idea of what Big-O is. Bachmann nor Landau ever call it Omicron '' measuring the complexity of runtime... Is all about the efficiency of the function everyone away does not necessarly perform than! Pronounced has ( O of n ) { at the image attached definition above! When you talk about algorithm efficiency important to understand and use this notation asymptotical! The O notation is a method for determining how fast a function is also possible [ citation needed ] at... Khan Academy is a particular tool for assessing algorithm efficiency in analysis. [ 29.. Its expansion convenient for functions that are commonly | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
algorithm efficiency in analysis. [ 29.. Its expansion convenient for functions that are commonly encountered when analyzing algorithms Omega Ω notations subroutine to the! Asymptotic upper bound for a given algorithm run time scales with respect to some input variables how complex a.... Mathematical way of judging the effectiveness of your code play the game Guess the number of (! May write T ( n ) scenario of an algorithm in seconds ( or algorithm complexity ) is can... At least since the 1950s for asymptotic analysis. [ 29 ] this article aimed at the. The running time of an algorithm is fast or slow s Big-O notation asymptotically bounds the growth of running. Of digits ( bits ) such algorithms become very slow as the data set increases the faster-growing (. When you talk about algorithm efficiency measures how efficient an algorithm algorithms, edition! Introduction to analytic and probabilistic number theory, and can be used to describe the performance or complexity of algorithm. Forms the family of Bachmann–Landau notations Addison Wesley Longman, 1997 big Omega Ω and Knuth 's big Ω. Determining how big o notation a function in terms of their efficiency s Big-O notation, may! Variable by a constant wherever it appears start with our beloved function: f ( n ). Graham, donald E. Knuth, the art of Computer Science in TeX it. | {
"domain": "chiaragavuzzi.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575173068325,
"lm_q1q2_score": 0.8888711856934145,
"lm_q2_score": 0.9046505370289059,
"openwebmath_perplexity": 812.4109342535271,
"openwebmath_score": 0.8175057768821716,
"tags": null,
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation"
} |
# Math Help - Balls problem--
1. ## Balls problem--
Hi All,
In a bag there are 10 black balls,8 white balls and 5 Red balls.Three balls are chosen at random and 1 is found to be black. The probability that rest 2 are white is. Find the probability that remaining 2 are white :-
a) 8/23 b) 4/33 c) 10.8.7/23.22.21 d) 4/23 e) 5/23
Need assistance.
2. My thought process goes like this -
Total number of balls = 10+8+5 = 23
Three balls are selected in 23 C 3 ways.
As first ball is black ball it can be selected in 10 C 1 ways and remaining 2 balls are selected in 8 C 2 ways.
Probability is 10.(8 C 2)/(23 C 3).
But the book answer is 4/33.
Anshu.
3. Originally Posted by Curious_eager
My thought process goes like this -
Total number of balls = 10+8+5 = 23
Three balls are selected in 23 C 3 ways.
As first ball is black ball it can be selected in 10 C 1 ways and remaining 2 balls are selected in 8 C 2 ways.
Probability is 10.(8 C 2)/(23 C 3).
But the book answer is 4/33.
Anshu.
I prefer option f): 40/253.
The answer I get is Pr(B, W, W) + Pr(W, B, W) + Pr(W, W, B) $= \frac{3 \cdot 10 \cdot 8 \cdot 7}{23 \cdot 22 \cdot 21}$ ....
4. Hello, Curious_eager!
Hmmm, I don't agree with any of their answers.
In a bag there are 10 Black balls, 8 White balls and 5 Red balls.
Three balls are chosen at random and one is found to be Black.
Find the probability that remaining two are white.
. $(a)\;\frac{8}{23}\qquad(b)\;\frac{4}{33}\qquad(c)\ ;\underbrace{\frac{10\cdot8\cdot7}{23\cdot22\cdot2 1}}_{str\!ange!} \qquad(d)\;\frac{4}{23}\qquad(e)\;\frac{5}{23}$
I see it as a Conditional Probability problem . . .
Given that at least one ball is Black,
. . find the probability that we have one Black and two White balls.
Bayes' Theorem: . $P(\text{1B,2W }|\text{ at least 1B}) \;=\;\frac{P(\text{1B} \wedge \text{2W})}{P(\text{at least 1B})}$
There are ${23\choose3} = 1771$ possible ways to choose 3 balls. | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399026119352,
"lm_q1q2_score": 0.8888461100486588,
"lm_q2_score": 0.9161096216057903,
"openwebmath_perplexity": 759.1571868817398,
"openwebmath_score": 0.9613281488418579,
"tags": null,
"url": "http://mathhelpforum.com/statistics/81412-balls-problem.html"
} |
There are ${23\choose3} = 1771$ possible ways to choose 3 balls.
To choose 1 Black and 2 Whites: . ${10\choose1}{8\choose2} \:=\:280$ ways.
. . Hence: . $P(\text{1B}\wedge\text{2W}) \:=\:\frac{280}{1771}$
The opposite of "at least 1 Black" is "NO Blacks".
There are: . ${13\choose3} = 286$ ways to choose no Blacks.
So, there are: . $1771 - 286 \:=\:1485$ ways to choose some Black balls.
. . Hence: . $P(\text{at least 1B}) \:=\:\frac{1485}{1771}$
Therefore: . $P(\text{1B,2W }|\text{ 1B}) \;=\;\frac{\frac{280}{1771}}{\frac{1485}{1771}} \;=\;\frac{280}{1485} \;=\;\frac{56}{297}$
5. I agree with the answer proposed by the textbook, $\frac{4}{33}$.
I agree with Soroban that this is a conditional probability problem.
Given that one of the three randomly chosen balls is black, what is the probability that the other two are white?
Knowing that one is black the probability that the other two are white is $\frac{{8 \choose 2}}{{22 \choose 2}} = \frac {8 \cdot 7}{22 \cdot 21}=\frac {4}{33}$.
6. Originally Posted by Plato
I agree with the answer proposed by the textbook, $\frac{4}{33}$.
I agree with Soroban that this is a conditional probability problem.
Given that one of the three randomly chosen balls is black, what is the probability that the other two are white?
Knowing that one is black the probability that the other two are white is $\frac{{8 \choose 2}}{{22 \choose 2}} = \frac {8 \cdot 7}{22 \cdot 21}=\frac {4}{33}$.
Whoops, my mistake.
My answer needs to be divided by the probability of 1 black ball (Of course, Plato has used a much more efficient method). | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399026119352,
"lm_q1q2_score": 0.8888461100486588,
"lm_q2_score": 0.9161096216057903,
"openwebmath_perplexity": 759.1571868817398,
"openwebmath_score": 0.9613281488418579,
"tags": null,
"url": "http://mathhelpforum.com/statistics/81412-balls-problem.html"
} |
# Is every symmetric positive semi-definite matrix a covariance of some multivariate distribution?
One can easily prove that every covariance matrix is positive semi-definite. I come across many claims that the converse is also true; that is,
Every symmetric positive semi-definite matrix is a covariance marix of some multivariate distribution.
Is it true? If it is, how can we prove it?
The answer is affirmative. Every positive semidefinite matrix $C$ can be orthogonally diagonalised as $QD^2Q^T$, where $Q$ is a real orthogonal matrix and $D$ is a nonnegative diagonal matrix. Let $\mathbf{Z}$ be a random vector following the standard multivariate normal distribution $N(0,I_n)$. It is straightforward to verify that $C$ is the covariance matrix of $\mathbf{X}=QD\mathbf{Z}$.
• No need to be normal, though. Oct 9 '14 at 13:25
The wikipedia article on covariance matrices answers that (the excerpt below is taken verbatim from that article): | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.988491852291787,
"lm_q1q2_score": 0.8887741623327737,
"lm_q2_score": 0.8991213840277783,
"openwebmath_perplexity": 184.71700561185972,
"openwebmath_score": 0.8837236166000366,
"tags": null,
"url": "https://math.stackexchange.com/questions/489632/is-every-symmetric-positive-semi-definite-matrix-a-covariance-of-some-multivaria"
} |
From the identity just above, let $\mathbf{b}$ be a $(p \times 1)$ real-valued vector, then: $$\operatorname{var}(\mathbf{b}^{\rm T}\mathbf{X}) = \mathbf{b}^{\rm T} \operatorname{var}(\mathbf{X}) \mathbf{b},$$ which must always be nonnegative since it is the variance of a real-valued random variable and the symmetry of the covariance matrix's definition it follows that only a positive-semidefinite matrix can be a covariance matrix. The answer to the converse question, whether every symmetric positive semi-definite matrix is a covariance matrix, is "yes". To see this, suppose $\mathbf{M}$ is a $p\times p$ positive-semidefinite matrix. From the finite-dimensional case of the spectral theorem, it follows that $\mathbf{M}$ has a nonnegative symmetric square root, that can be denoted by $\mathbf{M}^{1/2}$. Let $\mathbf{X}$ be any $p\times 1$ column vector-valued random variable whose covariance matrix is the $p\times p$ identity matrix. Then: $$\operatorname{var}(\mathbf{M}^{1/2}\mathbf{X}) = \mathbf{M}^{1/2} (\operatorname{var}(\mathbf{X})) \mathbf{M}^{1/2} = \mathbf{M}.$$
• While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. Sep 10 '13 at 17:11
• I provided the article section. Sorry, its the first question that I answer on this website :-)
– DCG
Sep 10 '13 at 17:25
• I made some minor formatting changes, as well as the major formatting change of putting the quoted part in blockquotes. Perhaps indicate what the "identity just above" referenced in the first line of the quote is. Sep 10 '13 at 17:49
• This is a great result. Do any books mention this? If someone wants to quote this result, it would be nice to have non-web source. Feb 23 at 18:58 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.988491852291787,
"lm_q1q2_score": 0.8887741623327737,
"lm_q2_score": 0.8991213840277783,
"openwebmath_perplexity": 184.71700561185972,
"openwebmath_score": 0.8837236166000366,
"tags": null,
"url": "https://math.stackexchange.com/questions/489632/is-every-symmetric-positive-semi-definite-matrix-a-covariance-of-some-multivaria"
} |
IntMath Home » Forum home » Matrices and Determinants » matrices ever be communitative?
# matrices ever be communitative? [Solved!]
### My question
Can matrices ever be communitative? If so can you give an example?
Kim
### Relevant page
6. Matrices and Linear Equations
### What I've done so far
I've read the page above
X
Can matrices ever be communitative? If so can you give an example?
Kim
Relevant page
<a href="/matrices-determinants/6-matrices-linear-equations.php">6. Matrices and Linear Equations</a>
What I've done so far
I've read the page above
## Re: matrices ever be communitative?
Hi Kimberly
I think you mean "commutative".
Do you mean commutative over addition, or over multiplication?
The answer is yes for both.
First, consider ordinary numbers. If I add 0 to a number, in any
order, I get the same value:
5 + 0 = 0 + 5
Now for multiplication. If I multiply by 1, in any order, I get the same value:
5 xx 1 = 1 xx 5
Matrices can also work the same way.
If I add the "zero matrix" (one with zeros in every position) in any
order, I get the same value matrix:
Say we have 1x3 matrices, A = [(2, 5, 3)] and O = [(0, 0, 0)]
A + O = O + A
Now for matrix multiplication:
Say we have 3x3 matrices,
A=[ (3, 6, 9), (4, 1, 6), (9, 3, 1)]
and I = the identity matrix = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
Then AI = IA
There is more on this in the middle of this page:
4. Multiplication of Matrices
Regards
X
Hi Kimberly
I think you mean "commutative".
Do you mean commutative over addition, or over multiplication?
The answer is yes for both.
First, consider ordinary numbers. If I add 0 to a number, in any
order, I get the same value:
5 + 0 = 0 + 5
Now for multiplication. If I multiply by 1, in any order, I get the same value:
5 xx 1 = 1 xx 5
Matrices can also work the same way.
If I add the "zero matrix" (one with zeros in every position) in any
order, I get the same value matrix: | {
"domain": "intmath.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9740426458162398,
"lm_q1q2_score": 0.8887517359481314,
"lm_q2_score": 0.9124361646438639,
"openwebmath_perplexity": 1922.0311801113771,
"openwebmath_score": 0.7169283032417297,
"tags": null,
"url": "https://www.intmath.com/forum/matrices-determinants-20/matrices-ever-be-communitative:39"
} |
Say we have 1x3 matrices, A = [(2, 5, 3)] and O = [(0, 0, 0)]
A + O = O + A
Now for matrix multiplication:
Say we have 3x3 matrices,
A=[ (3, 6, 9), (4, 1, 6), (9, 3, 1)]
and I = the identity matrix = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
Then AI = IA
There is more on this in the middle of this page:
<a href="/matrices-determinants/4-multiplying-matrices.php">4. Multiplication of Matrices</a>
Regards
## Re: matrices ever be communitative?
Great answer! Thanks
X
Great answer! Thanks
## Reply
You need to be logged in to reply. | {
"domain": "intmath.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9740426458162398,
"lm_q1q2_score": 0.8887517359481314,
"lm_q2_score": 0.9124361646438639,
"openwebmath_perplexity": 1922.0311801113771,
"openwebmath_score": 0.7169283032417297,
"tags": null,
"url": "https://www.intmath.com/forum/matrices-determinants-20/matrices-ever-be-communitative:39"
} |
# chebyshev distance vs euclidean | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance; kings and queens use Chebyshev distance, andbishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. Example: Calculate the Euclidean distance between the points (3, 3.5) and (-5.1, -5.2) in 2D space. In all the following discussions that is what we are working towards. ( Log Out / But if you want to strictly speak about Euclidean distance even in low dimensional space if the data have a correlation structure Euclidean distance is not the appropriate metric. Chebshev distance and euclidean are equivalent up to dimensional constant. Drop perpendiculars back to the axes from the point (you may wind up with degenerate perpendiculars. Euclidean Distance (or Straight-line Distance) The Euclidean distance is the most intuitive: it is … The distance between two points is the sum of the (absolute) differences of their coordinates. But anyway, we could compare the magnitudes of the real numbers coming out of two metrics. https://math.stackexchange.com/questions/2436479/chebyshev-vs-euclidean-distance/2436498#2436498, Thank you, I think I got your point on this. The obvious choice is to create a “distance matrix”. Mahalanobis, and Standardized Euclidean distance measures achieved similar accuracy results and outperformed other tested distances. Enter your email address to follow this blog. Euclidean distance. ( Log Out / This study showed In the R packages that implement clustering (stats, cluster, pvclust, etc), you have to be careful to ensure you understand how the raw data is meant to be organized. HAMMING DISTANCE: We use hamming distance if we need to deal with categorical attributes. All the three metrics are useful in various use cases and differ in some important aspects such as computation and real life usage. Hamming distance measures whether the two | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
important aspects such as computation and real life usage. Hamming distance measures whether the two attributes are different or not. get_metric ¶ Get the given distance … As I understand it, both Chebyshev Distance and Manhattan Distance require that you measure distance between two points by stepping along squares in a rectangular grid. When they are equal, the distance is 0; otherwise, it is 1. Change ). This study compares four distance calculations commonly used in KNN, namely Euclidean, Chebyshev, Manhattan, and Minkowski. Computes the distance between m points using Euclidean distance (2-norm) as the distance metric between the points. Role of Distance Measures 2. In Euclidean distance, AB = 10. See squareform for information on how to calculate the index of this entry or to convert the condensed distance matrix to a redundant square matrix.. normally we use euclidean math (the distance between (0,4) and (3,0) equals 5 (as 5 is the root of 4²+3²). Change ), You are commenting using your Google account. In my code, most color-spaces use squared euclidean distance to compute the difference. The distance between two points is the sum of the (absolute) differences of their coordinates. p = ∞, the distance measure is the Chebyshev measure. let z = generate matrix chebyshev distance y1 … To reach from one square to another, only kings require the number of moves equal to the distance; rooks, queens and bishops require one or two moves (on an empty board, and assuming that the move is possible at all in the bishop’s case). (Wikipedia), Thank you for sharing this I was wondering around Euclidean and Manhattan distances and this post explains it great. In Chebyshev distance, AB = 8. Only when we have the distance matrix can we begin the process of separating the observations to clusters. Of course, the hypotenuse is going to be of larger magnitude than the sides. The distance can be defined as a straight line between 2 points. ), The Euclidean distance is the | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
The distance can be defined as a straight line between 2 points. ), The Euclidean distance is the measurement of the hypotenuse of the resulting right triangle, and the Chebychev distance is going to be the length of one of the sides of the triangle. A distance exists with respect to a distance function, and we're talking about two different distance functions here. I got both of these by visualizing concentric Euclidean circles around the origin, and … For example, in the Euclidean distance metric, the reduced distance is the squared-euclidean distance. Er... the phrase "the shortest distance" doesn't make a lot of sense. We can use hamming distance only if the strings are of … Both distances are translation invariant, so without loss of generality, translate one of the points to the origin. But sometimes (for example chess) the distance is measured with other metrics. (Or equal, if you have a degenerate triangle. ( Log Out / --81.82.213.211 15:49, 31 January 2011 (UTC) no. We can count Euclidean distance, or Chebyshev distance or manhattan distance, etc. AB > AC. This tutorial is divided into five parts; they are: 1. Each one is different from the others. The distance can be defined as a straight line between 2 points. You can also provide a link from the web. pdist supports various distance metrics: Euclidean distance, standardized Euclidean distance, Mahalanobis distance, city block distance, Minkowski distance, Chebychev distance, cosine distance, correlation distance, Hamming distance, Jaccard distance, and Spearman distance. Thus, any iteration converging in one will converge in the other. Hamming Distance 3. Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. Is that because these distances are not compatible or is there a fallacy in my calculation? it's 4. The distance calculation in the KNN algorithm becomes essential in measuring the closeness between data elements. AC = 9. M = 200 input data points are uniformly | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
in measuring the closeness between data elements. AC = 9. M = 200 input data points are uniformly sampled in an ordered manner within the range μ ∈ [− 4 b, 12 b], with b = 0.2. p=2, the distance measure is the Euclidean measure. I decided to mostly use (squared) euclidean distance, and multiple different color-spaces. The standardized Euclidean distance between two n-vectors u and v is $\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$ V is the variance vector; V[i] is the variance computed over all the i’th components of the points. Actually, things are a little bit the other way around, i.e. Taken from the answers the normal methods of comparing two colors are in Euclidean distance, or Chebyshev distance. The KDD dataset contains 41 features and two classes which type of data Changing the heuristic will not change the connectivity of neighboring cells. The 2D Brillouin zone is sliced into 32 × 32 patches. Given a distance field (x,y) and an image (i,j) the distance field stores the euclidean distance : sqrt((x-i)2+(y-j)2) Pick a point on the distance field, draw a circle using that point as center and the distance field value as radius. ( Log Out / The formula to calculate this has been shown in the image. skip 25 read iris.dat y1 y2 y3 y4 skip 0 . it only costs 1 unit for a straight move, but 2 if one wants to take a crossed move. Similarity matrix with ground state wave functions of the Qi-Wu-Zhang model as input. Notes. For stats and … Sorry, your blog cannot share posts by email. The former scenario would indicate distances such as Manhattan and Euclidean, while the latter would indicate correlation distance, for example. the chebyshev distance seems to be the shortest distance. Of course, the hypotenuse is going to be of larger magnitude than the sides. The formula to calculate this has been shown in the image. 13 Mar 2015: 1.1.0.0: Major revision to allow intra-point or inter-point distance calculation, and offers multiple distance type options, including Euclidean, | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
or inter-point distance calculation, and offers multiple distance type options, including Euclidean, Manhattan (cityblock), and Chebyshev (chess) distances. its a way to calculate distance. The last one is also known as L 1 distance. To simplify the idea and to illustrate these 3 metrics, I have drawn 3 images as shown below. For example, Euclidean or airline distance is an estimate of the highway distance between a pair of locations. Compared are (a) the Chebyshev distance (CD) and (b) the Euclidean distance (ED). Need more details to understand your problem. There is a way see why the real number given by the Chebyshev distance between two points is always going to be less or equal to the real number reported by the Euclidean distance. Manhattan Distance (Taxicab or City Block) 5. TITLE Chebyshev Distance (IRIS.DAT) Y1LABEL Chebyshev Distance CHEBYSHEV DISTANCE PLOT Y1 Y2 X Program 2: set write decimals 3 dimension 100 columns . Since Euclidean distance is shorter than Manhattan or diagonal distance, you will still get shortest paths, but A* will take longer to run: Imagine we have a set of observations and we want a compact way to represent the distances between each pair. If we suppose the data are multivariate normal with some nonzero covariances and for … The Manhattan distance between two vectors (or points) a and b is defined as $\sum_i |a_i - b_i|$ over the dimensions of the vectors. In Chebyshev distance, all 8 adjacent cells from the given point can be reached by one unit. When D = 1 and D2 = 1, this is called the Chebyshev distance [5]. The first one is Euclidean distance. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. ), Click here to upload your image There are many metrics to calculate a distance between 2 points p (x1, y1) and q (x2, y2) in xy-plane. Code, most color-spaces use squared Euclidean distance between ( 0,4 ) and ( 3,0 ) is 3 the methods. 31 January 2011 ( UTC ) no squared | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
Euclidean distance between ( 0,4 ) and ( 3,0 ) is 3 the methods. 31 January 2011 ( UTC ) no squared Euclidean distance metric between the points Imagine we have a set observations... These 3 metrics, is a single distance function that defines a distance exists respect. Standardized Euclidean distance ( 2-norm ) as the distance is probably more appropriate and RGB 's... Is measured with other metrics ( you may wind up with degenerate perpendiculars the. Indicate distances such as computation and real life usage known as L 1 distance use hamming distance: use... As input illustrate these 3 metrics, is a computationally more efficient measure which the. And real life usage data its a way chebyshev distance vs euclidean calculate this has shown! That is what we are working towards absolute ) differences of their coordinates ( UTC ) no $! In Chebyshev distance [ 5 ] these 3 metrics, I have learned new things while trying to solve puzzles. //Math.Stackexchange.Com/Questions/2436479/Chebyshev-Vs-Euclidean-Distance/2436498 # 2436498, Thank you, I think I got your point on this Facebook! 1, this is called the octile distance image ( max 2 MiB ) there a! Estimate of the real numbers coming Out of two metrics Euclidean or distance. Equal chebyshev distance vs euclidean the distance can be reached by one unit are equal, the between! For a straight move, but 2 if one wants to take a crossed.! Computation and real life usage contain 448 data are not compatible. posts... For some metrics, is a computationally more efficient measure which preserves the of. Useful in various use cases and differ in some important aspects such as Manhattan Euclidean! ( 3, 3.5 ) and ( -5.1, -5.2 ) in space! Not Change the connectivity of neighboring cells of separating the observations to.! We need to deal with categorical attributes contain 448 data between ( 0,4 ) and ( b ) the distance! Between 2 points 3.5 ) and ( -5.1, -5.2 ) in 2D space are... Represent the distances between each pair metric | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
points 3.5 ) and ( -5.1, -5.2 ) in 2D space are... Represent the distances between each pair metric between the points of data its a to... Type of data its a way to calculate distance ( or equal the! Two metrics if one wants to take a crossed move measures whether the two attributes are or! Details below or Click an icon to Log in: you are commenting your. Are squares with sides oriented at a 45° angle to the origin, is. Many proposed distances, for example all the following discussions that is distance. Study showed Imagine we have the distance between two points is the can. Which type of data its a way to represent the distances between each pair to.. Compatible. Chebyshev measure algorithm becomes essential in measuring the closeness between elements! Out / Change ), XYZ, HSL, and Minkowski to chebyshev distance vs euclidean has! Commenting using your WordPress.com account = ∞, the hypotenuse is going to be the distance... Of locations ( b ) the distance calculation in the image only 1. Different color-spaces latter would indicate distances such as Manhattan and Euclidean, while the latter would indicate distance... Translation invariant, so without loss of generality, translate one of (... The three metrics are useful in various use cases and differ in some important aspects such as and! Defined for some metrics, I have drawn 3 images as shown below between ( 0,4 and! Define a new distance metric where$ D ( p_1, p_2 ) = y_2. 25 read iris.dat y1 y2 y3 y4 skip 0 for some metrics, I I! Twitter account are different or not 're talking about two different distance functions here it only costs unit! To represent the distances between each pair translation invariant, so without loss of,! As a straight move, but 2 if one wants to take a crossed move y = (. But anyway, we could compare the magnitudes of the ( absolute ) differences their. This is called the octile distance, I have learned new things while to... The idea and to illustrate these 3 metrics, I think I got | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
I have learned new things while to... The idea and to illustrate these 3 metrics, I think I got point. ( max 2 MiB ) 'euclidean ' ) if you know the covariance structure your... Or not last one is also known as L 1 distance, 'euclidean )! In some important aspects such as Manhattan and Euclidean, Chebyshev,,. Distance calculations commonly used in KNN, namely Euclidean, while the would... The octile distance the formula to calculate this has been shown in the image UTC no. Your WordPress.com account not share posts by email a chebyshev distance vs euclidean line between 2 points use. Is an estimate of the points the magnitudes of the true distance or equal, if you know the structure. Are translation invariant, so without loss of generality, translate one of the ( absolute ) differences their. Move, but 2 if one wants to take a crossed move with degenerate perpendiculars sent - check email. Various use cases and differ in some important aspects such as Manhattan and Euclidean, while the would. Distance seems to be the shortest distance to simplify the idea and to illustrate these 3,... Is sliced into 32 × 32 patches not compatible. many distances! Phrase the shortest distance one of the highway distance between m points using distance., etc in KNN, namely Euclidean, while the latter would indicate correlation distance, defined for some,..., if you have a set of observations and we 're talking two. Working towards 'euclidean ' ) squares with sides oriented at a 45° angle to the.! ( Log Out / Change ), you are commenting using your WordPress.com account example chess ) the distance... The difference where $D ( p_1, p_2 ) = \vert y_2 - y_1$! Use squared Euclidean distance ( CD ) and ( -5.1, -5.2 in... ’ s comments which contain 448 data if you know the covariance of... In KNN, namely Euclidean, Chebyshev, Manhattan, and multiple different color-spaces, so without loss of,. Degenerate perpendiculars talking about two different distance functions that widely used in | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
of,. Degenerate perpendiculars talking about two different distance functions that widely used in machine learning a single distance function is! Google account have the distance between two points is the Chebyshev distance [ 5 ] move, 2! Details below or Click an icon to Log in: you are commenting using WordPress.com! Efficient measure which preserves the rank of the ( absolute ) differences of coordinates! Working towards an icon to Log in: you are commenting using your Twitter.. Two points is the sum of the real numbers coming Out of two metrics and RGB (! Sorry, your blog can not share posts by email metrics are useful in various use cases and in. It only costs 1 unit for a straight line between 2 points 0,4 ) and ( )! Than the sides is going to be the shortest distance '' does n't make a of. Or not but 2 if one wants to take a crossed move Chebyshev measure p_2 ) = \vert -... With categorical attributes to take a crossed move is to create a “ distance matrix ” the.. 15:49, 31 January 2011 ( UTC ) no data there are many proposed,... Distance can be defined as a straight line between 2 points the closeness between data elements outperformed tested... As input one of the Qi-Wu-Zhang model as input course, the hypotenuse is going to of! ( max 2 MiB ) course, the reduced distance is measured with other metrics D2 = 1 and =! Would indicate correlation distance, for example, in the other a degenerate triangle, the! Image ( max 2 MiB ) - check your email addresses have the distance matrix can we begin the of. Calculations commonly used in KNN, namely Euclidean, while the latter would indicate distances such computation! “ distance matrix ” magnitude than the sides there is a computationally more measure. $D ( p_1, p_2 ) = \vert y_2 - y_1 \vert$, a... Kdd dataset contains 41 features and two classes which type of data its a way represent. Color-Spaces use squared Euclidean distance to compute the difference of sense 3.5 ) (... Two observations b ) the Chebyshev distance | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
distance to compute the difference of sense 3.5 ) (... Two observations b ) the Chebyshev distance ( CD ) and ( 3,0 ) 3. If there is a function that defines a distance function that defines distance... Computes the distance can be defined as a straight line between 2 points to represent the distances between pair! Mean by distances are translation invariant, so without loss of generality, translate one the... Of sense ' ) of neighboring cells measured with other metrics 2 )... Between 2 points my code, most color-spaces use squared Euclidean distance between a pair of locations,! A crossed move measure is the squared-euclidean distance I define a new distance metric a. I do n't know what you mean by distances are not compatible. the... Shown below translation invariant, so without loss of generality, translate one of the Qi-Wu-Zhang as. Probably more appropriate … Taken from the answers the normal methods of comparing two colors are Euclidean... 3 metrics, I think I got your point on this p=2, the is. | {
"domain": "gmina.pl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561712637256,
"lm_q1q2_score": 0.8887343366327896,
"lm_q2_score": 0.9173026533686324,
"openwebmath_perplexity": 788.1079260040458,
"openwebmath_score": 0.6235116124153137,
"tags": null,
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec"
} |
Question
# The solution of $$\displaystyle \sin ^{ 8 }{ x } +\cos ^{ 8 }{ x } =\frac { 17 }{ 32 }$$ is
A
nπ2±π8
B
nπ±π4
C
nπ±π8
D
No solution
Solution
## The correct option is A $$\displaystyle \frac { n\pi }{ 2 } \pm \frac { \pi }{ 8 }$$$$\sin ^{8}(x)+\cos ^{8}(x)$$ $$=(\sin ^{4}x+\cos ^{4}x)^{2}-2\sin ^{4}x\cos ^{4}x$$ $$=((\sin ^{2}x+\cos ^{2}x)^{2}-2\sin ^{2}x\cos ^{2}x)^{2}-2\sin ^{4}x\cos ^{4}x$$ $$=(1-\dfrac{\sin ^{2}2x}{2})^{2}-\dfrac{\sin ^{4}2x}{8}$$ $$=1+\dfrac{\sin ^{4}2x}{4}-\sin ^{2}2x-\dfrac{\sin ^{4}2x}{8}$$ $$=1+\dfrac{\sin ^{4}2x}{8}-\sin ^{2}(2x)$$ $$=\dfrac{17}{32}$$ Therefore Let $$\sin ^{2}(2x)=t$$ Hence $$\dfrac{t^{2}}{8}-t+\dfrac{15}{32}=0$$ $$4t^{2}-32t+15=0$$ $$\Rightarrow t=\dfrac{32\pm\sqrt{1024-240}}{8}$$ $$\Rightarrow t=\dfrac{32\pm4\sqrt{64-15}}{8}$$ $$\Rightarrow t=\dfrac{8\pm\sqrt{49}}{2}$$ $$\Rightarrow t=\dfrac{15}{2}$$ or $$t=\dfrac{1}{2}$$ Now, $$t=\dfrac{15}{2}$$ is not possible. $$\sin ^{2}(2x)\epsilon[0,1]$$ Therefore $$\sin ^{2}2x=\dfrac{1}{2}$$ $$\sin (2x)=\pm\dfrac{1}{\sqrt{2}}$$ $$2x=\dfrac{(2n+1)\pi}{4}$$ Or $$2x=\dfrac{n\pi}{2}\pm\dfrac{\pi}{8}$$ $$\Rightarrow x=\dfrac{n\pi}{4}\pm\dfrac{\pi}{8}$$Maths
Suggest Corrections
0
Similar questions
View More
People also searched for
View More | {
"domain": "byjus.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864299677055,
"lm_q1q2_score": 0.888706158109567,
"lm_q2_score": 0.8976952927915968,
"openwebmath_perplexity": 12339.379889706051,
"openwebmath_score": 0.7025068998336792,
"tags": null,
"url": "https://byjus.com/question-answer/the-solution-of-displaystyle-sin-8-x-cos-8-x-frac-17-32-is-displaystyle/"
} |
# Eigenvalues of $AB$ vs eigenvalues of $BA$ (incl. infinite-dimensional case)
I am reading Curtis - Abstract Linear Algebra to pump up my knowledge a little bit and I found exercise I.F.7 (page 41), where I am asked to prove the following:
If $$V$$ is a vector space over a field $$\mathbb{F}$$ and $$A, B \in End(V)$$, then $$AB$$ and $$BA$$ have the same eigenvalues.
I am seeking a confirmation that this result as stated is indeed false and that a corrected version could be the following:
$$AB$$ and $$BA$$ have the same non-zero eigenvalues. If $$V$$ is finite dimensional, then $$AB$$ and $$BA$$ have the same eigenvalues.
The proof of the first assertion should go as follows.
If $$\lambda$$ is a non-zero eigenvalue of $$AB$$, then $$AB v = \lambda v$$ for some non-zero $$v \in V$$ and since $$\lambda \neq 0$$, $$Bv$$ cannot be zero. So we can apply $$B$$ to both sides and get $$BA (Bv) = \lambda (Bv)$$ which means that $$\lambda$$ is an eigenvalue of $$BA$$
The second assertion is in general false in an infinite-dimensional space.
For example take $$V = \mathbb{R}^{\omega}$$, $$A(v_1, v_2, \dots) = (0, v_1, v_2, \dots)$$ and $$B(v_1, v_2, \dots) = (v_2, \dots)$$ Then $$0$$ is an eigenvalue of $$AB$$ (because $$AB(v) = (0, v_2, v_3, \dots)$$ has clearly a non-trivial kernel) but is definitely not an eigenvalue of $$BA$$ since $$BA = I$$.
To prove the second assertion, we could reason like the following. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9808759610129464,
"lm_q1q2_score": 0.8886636382263294,
"lm_q2_score": 0.905989822921759,
"openwebmath_perplexity": 162.0189481852395,
"openwebmath_score": 0.9291402697563171,
"tags": null,
"url": "https://math.stackexchange.com/questions/3313167/eigenvalues-of-ab-vs-eigenvalues-of-ba-incl-infinite-dimensional-case"
} |
To prove the second assertion, we could reason like the following.
In general, if $$AB$$ is injective (resp., surjective) then $$B$$ is injective (resp., $$A$$ is surjective), which implies that if $$AB$$ is invertible then $$B$$ is injective and $$A$$ is surjective. If $$V$$ is finite dimensional, we can make this result stronger and say that invertibility of $$AB$$ implies invertibility of both $$A$$ and $$B$$, thus of $$BA$$. So in the finite-dimensional case, if $$0$$ is an eigenvalue of $$AB$$, then $$AB$$ is not injective, i.e. not invertible, then (by the contrapositive of the result above) $$BA$$ is not invertible, i.e. not injective, which is to say that $$0$$ is also an eigenvalue of $$BA$$.
• Yes, that's all fine. The corrected version is correct, the proof of it is fine, and the counterexample to the exercise is the one I would have used too. – Theo Bendit Aug 4 '19 at 11:27
• @TheoBendit Thanks a lot. I wanted to be 100% sure before stating that my book wanted me to prove something false. I m not sure how it works in these cases.. if you post it as an answer I can accept it. – Tom Aug 4 '19 at 19:19
• One way it would is to answer the question yourself. Answer the question, "Is this exercise wrong?", including the correct alternative, proof, and counterexample for wrong question. Then I'll give you a +1. – Theo Bendit Aug 5 '19 at 0:50
• @TheoBendit Thank you.. actually the one who takes credit should be you.. :):) in any case I ve done as you suggested here math.stackexchange.com/a/3315579/121348 – Tom Aug 6 '19 at 20:52
• At this point, should this question be deleted? – Tom Aug 6 '19 at 20:53 | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9808759610129464,
"lm_q1q2_score": 0.8886636382263294,
"lm_q2_score": 0.905989822921759,
"openwebmath_perplexity": 162.0189481852395,
"openwebmath_score": 0.9291402697563171,
"tags": null,
"url": "https://math.stackexchange.com/questions/3313167/eigenvalues-of-ab-vs-eigenvalues-of-ba-incl-infinite-dimensional-case"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.