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Let $\{ \psi_{j,k}(t)\} haar system. How to prove that it is orthogonal? |
Let $\psi_{j,k}(t)= \left \{ \begin{array}{ll} 2^{j/2} &, 2^{-j}k < t < 2^{-j}(k+1/2) \\-2^{j/2} &, 2^{-j}(k+1/2) < t < 2^{-j}(k+1) \\ 0, \textrm{otherwise} \end{array} \right$. How to prove that it is orthogonal? In other words how to prove that $\langle \psi_{j_1,k_1}(t), \psi_{j_2, k_2}(t) \rangle = 0$, $j_1<j_2$ a... |
As Rasmus points out, once you state the result correctly, it's easy -assuming you've already proved some elementary properties of homotopy.
Namely, let $f,g$ be two loops with $f(0) = g(0) = f(1)= g(1) = x_0$ and such that $g^{-1}*f \sim 1$, where $1$ is the constant path at $x_0$.
Then $f\sim 1* f \sim (g*g^{-1... |
Let $\{ \psi_{j,k}(t)\}$ haar system. How to prove that it is orthogonal? |
Say $M := \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ is a block matrix with $A, D$ being square matrices and thus $B$ and $C^T$ having the same shape. Is there any norm characterizing the collection of $B$ and $C$ that is invariant under a similarity transformation of the whole block matrix? Were $B$ and $C$ square m... |
What are norms of sub-matrices invariant under a similarity transformation of a block matrix? |
Say $M := \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ is a block matrix with $A, D$ being square matrices and this $B$ and $C^T$ having the same shape. Is there any norm characterizing the collection of $B$ and $C$ that is invariant under a similarity transformation of the whole block matrix? Where $B$ and $C$ square ... |
Let $\psi_{j,k}(t)=\{ \begin{array}{ll} 2^{j/2} &, 2^{-j}k < t < 2^{-j}(k+1/2) \\-2^{j/2} &, 2^{-j}(k+1/2) < t < 2^{-j}(k+1) \\ 0, \textrm{otherwise} \end{array} $. How to prove that it is orthogonal? In other words how to prove that $\langle \psi_{j_1,k_1}(t), \psi_{j_2, k_2}(t) \rangle = 0$, $j_1<j_2$ and $k_1<k_2$.... |
Let $G \in \mathbf{Grp}$, $H \leq G$, $G/H := \lbrace gH: g \in G \rbrace$. We can then introduce group operation on $G/H$ as $(xH)(yH) := (xy)H$, so that $G/H$ becomes a quotient group when $H$ is a normal subgroup.
But why do we only work with quotient groups by normal subgroups? If we introduce the notion of _lef... |
Why do we define quotient groups for normal subgroups only? |
I'm working on data structure for graph cut algorithm. Problem is to make different cuts on shortest paths. I made data structure for which I'm not sure about properties.
Input is directed graph of shortest paths, which is bounded lattice, partially ordered set with minimum and maximum element.
Define _next node ... |
Wa are talking about [Non-uniform rational B-spline][1]. We have some simple 3 dimentional array like
{1,1,1}
{1,2,3}
{1,3,3}
{2,4,5}
{2,5,6}
{4,4,4}
Which are points froma plane created by some B-spline
How to find controll points of spline that created that plane? (I know its a ... |
How to get NURBS controll points from an array of points that should be part of its solution from controll points we are searching for? |
We are talking about [Non-uniform rational B-spline][1]. We have some simple 3 dimensional array like
{1,1,1}
{1,2,3}
{1,3,3}
{2,4,5}
{2,5,6}
{4,4,4}
Which are points from a plane created by some B-spline
How to find control points of spline that created that plane? (I know its a ... |
How to get NURBS control points from an array of points that should be part of its solution from controll points we are searching for? |
Let $G \in \mathbf{Grp}$, $H \leq G$, $G/H := \lbrace gH: g \in G \rbrace$. We can then introduce group operation on $G/H$ as $(xH)*(yH) := (xy)H$, so that $G/H$ becomes a quotient group when $H$ is a normal subgroup.
But why do we only work with quotient groups by normal subgroups? If we introduce the notion of _le... |
Let $X$ be a subspace of $\ell_1^4$. Can one always extend a linear operator $l:X\rightarrow \ell_1^4$
to $L:\ell_1^4\rightarrow \ell_1^4$ such that $L$ has the same operator norm as $l$?
Thanks! |
Wanted: Examples of how black box optimizer works - step by step? |
So, you want to compare (254)(847) and (383)(536) without actually computing the products, look at
$$\frac{847}{383} \; ? \; \frac{536}{254}$$
Multiplying both numerators by 2
$$\frac{847}{766} \; ? \; \frac{536}{508}$$
or
$$1+\frac{81}{766} \; ? \; 1+\frac{28}{508}$$
You are now left with comparing
... |
So, you want to compare (254)(847) and (383)(536) without actually computing the products, look at
$$\frac{847}{383} \; ? \; \frac{536}{254}$$
Multiplying both denominators by 2
$$\frac{847}{766} \; ? \; \frac{536}{508}$$
or
$$1+\frac{81}{766} \; ? \; 1+\frac{28}{508}$$
You are now left with comparing... |
I came across this problem in the context of spectroscopy today. Because of it's simplicity, I'm sure it's a question that's been posed by some mathematician ages ago, I just can't figure out how to formulate it mathematically:
Suppose you have a mirror that forms a perfect ring and has an aperture in it with width... |
You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll.
Question: What is the best strategy?
According to my calculation, for the strategy 6,5,5,4,4, the expected value is $142/27\approx 5.26$, which I consider quite high. So this might be th... |
We solve the pell equation using the continued fraction for square root of 2. What equations can we solve using the continued fraction of cube roots (and other numbers too)? |
Solving equations using continued fractions? |
In the worst case, where the comparison is close, you will always end up having to do as much work as multiplication. The performance gains from any non-worst-case improvements would have to be pretty good to make the programming effort worthwhile. Why do you need this? |
As Ross Millikan notes, this is a standard [Subset Sum](http://en.wikipedia.org/wiki/Subset_sum_problem) or [Number Partition Problem](http://en.wikipedia.org/wiki/Partition_problem) which are both [NP-Complete](http://en.wikipedia.org/wiki/NP-complete).
If your Subset Sum instance is $(a_0, a_1, \dots, a_{n-1})$, w... |
Say $M := \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ is a block matrix with $A, D$ being square matrices and this $B$ and $C^T$ having the same shape. Is there any norm characterizing the collection of $B$ and $C$ that is invariant under all blockdiagonal similarity transformations $M\to S M S^{-1}$ with $S=\begin{pm... |
What are norms of sub-matrices invariant under a blockdiagonal similarity transformation of a block matrix? |
You are looking for the [Halting Problem][1] and [Higher-order logic][4].
You can't really count the functions via their representations as programs, because you can neither compare all program behaviours nor find out all those programs that won't halt at all. You could define a function which is not only undefined ... |
Related questions arise frequently on sci.math, where I [often][1] point out the following standard reference on the topic.
Beware that this equivalence, i.e. $\rm\ aR = bR \iff a/b\ $ is a unit in $\rm\:R\:$,
generally fails when $\rm\:R\:$ has zero-divisors, so that there are at least a few different notions of ... |
1. Can a CFG over large alphabet describe a language, where each terminal appears even number of times?
2. If yes, would the Chomsky Normal Form be polynomial in |Σ| ?
Find a context-free grammar (CFG) for the language L of all
words such that each terminal in a word occurs even number of times over a possibly l... |
Can a CFG over large alphabet describe a language, where each terminal appears even number of times? |
You are looking for the [Halting Problem][1] and [Higher-order logic][4].
You can't really count the functions via their representations as programs, because you can neither compare all program behaviours nor find out all those programs that won't halt at all. You could define a function which is not only undefined ... |
What equivalence relation are you using to define motives?
The finest that people normally consider is rational equivalence, in which case
two morphisms whose graphs are rationally equivalent (which is to say, roughly speaking, two morphisms which can be deformed one into the other via a family parameterized by $\m... |
Let $R$ be a ring, $A$ is an ideal of $R$, and assume that $A\subseteq J(R)$. Let $r\longmapsto \overline{r}$ denote the coset map $R\rightarrow \overline{R}=R/A$. The following are equivalent:
(1) $A$ is lifting.
(2) If $\overline{R}=\overline{K_1}\oplus...\oplus \overline{K_n}$ where the $\overline{K_i}$ are l... |
The following is a plot comparing `Exp[Derivative[1,0][Zeta][0,x]+1/2Log[2 Pi]]` and `Gamma[x]`:
![alt text][1]
In theory the blue and the red graphs should be identical, giving the Gamma function. But in reality we have the blue plot (the plot of `Exp[Derivative[1,0][Zeta][0,x]+1/2Log[2 Pi]]`) representing the a... |
Generally such comparisons can be done efficiently via continued fractions, e.g.
$$\rm\displaystyle a = \frac{847}{383}\ =\ 2 + \cfrac{1}{4 + \cfrac{1}{1 + \cdots}}\ \ \Rightarrow\ \ 2+\frac{1}{4+1} < a < 2+\frac{1}4$$
$$\rm\displaystyle b = \frac{536}{254}\ =\ 2 + \cfrac{1}{9 + \cdots}\ \ \Rightarrow\ \ 2 < b ... |
Say $M := \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ is a block matrix with $A, D$ being square matrices and this $B$ and $C^T$ having the same shape. Is there any norm characterizing the collection of $B$ and $C$ that is invariant under all block diagonal similarity transformations $M\to S M S^{-1}$ with $S=\begin{p... |
What are norms of sub-matrices invariant under a block diagonal similarity transformation of a block matrix? |
Generally such comparisons can be done efficiently via continued fractions, e.g.
$$\rm\displaystyle a = \frac{847}{383}\ =\ 2 + \cfrac{1}{4 + \cfrac{1}{1 + \cdots}}\ \ \Rightarrow\ \ 2+\frac{1}{4+1} < a < 2+\frac{1}4$$
$$\rm\displaystyle b = \frac{536}{254}\ =\ 2 + \cfrac{1}{9 + \cdots}\ \ \Rightarrow\ \ 2 < b ... |
It is known that, for $n \geq 5$, it is possible to partition the integers $\{1, 2, \ldots, n\}$ into two disjoint subsets such that the product of the elements in one set equals the sum of the elements in the other. One solution is the following:
Let $N = \{1, 2, \ldots, n\}$.
If $n$ is even, take $P = \{1, \f... |
I'm trying to prove an identity involving the [digamma function](http://en.wikipedia.org/wiki/Digamma_function) $\psi(z)$, but I can't seem to figure out a way to do it. Can anyone help me out? The identity is
$$\psi\left(\frac{m}{2} + iy\right) + \psi\left(\frac{m}{2} - iy\right) = \psi\left(\frac{n}{2} + iy\right)... |
How would you expand a moment generating function with a negative fractional power as a power series??
What method would you be able to use? |
$2\times 2=4=2+2?$ |
If i have a graph in this form (adjacency matrix):
0 0 1 0 0 0 1<br />
0 0 0 1 0 1 0<br />
1 0 0 1 0 0 0<br />
0 1 1 0 0 0 0<br />
0 0 0 0 0 1 1<br />
0 1 0 0 1 0 0<br />
1 0 0 0 1 0 0<br />
This is a 2-regular graph with 7 vertices. What are examples of vertex invariants? Usually i would look at the degre... |
if $R$ is regular what is the relation between:
1) J(R)
2) a left $R$-module has a projective cover?!!!! |
Consider the game described [here][1], but for a sequence $X_1,\ldots,X_n$ of i.i.d. uniform rv's on $\lbrace 1,\ldots,n \rbrace$ (in the original game $n=6$). Using the original notation, let $a_n$ denote the first element in the best strategy $a_n,\ldots,a_2$. We saw that for $n=6$, $a_n = n$. Can you provide a heuri... |
A Lasker ring is a ring in which every ideal has a primary decomposition. The Lasker-Noether theorem states that every commutative Noetherian ring is a Lasker ring (as an easy consequence of the ascending chain condition). And I've found the statement that there are non-Noetherian Lasker rings, but I can't find an exam... |
Looking at <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069828">
the paper</a> referenced by Robin Chapman and Bill Dubuque in response to <a href="http://math.stackexchange.com/questions/14270/if-r-is-a-commutative-ring-with-identity-and-a-b-are-its-elem... |
Looking at <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069828">
the paper</a> referenced by Robin Chapman and Bill Dubuque in response to <a href="http://math.stackexchange.com/questions/14270/if-r-is-a-commutative-ring-with-identity-and-a-b-are-its-elem... |
A Lasker ring is a ring in which every ideal has a primary decomposition. The Lasker-Noether theorem states that every commutative Noetherian ring is a Lasker ring (as an easy consequence of the ascending chain condition). And I've found the statement that there are non-Noetherian Lasker rings, but I can't find an exam... |
I am truly lost as to what this problem is asking. I did post this on another forum and received what my have been wonderful advice. However, even after multiple hours and many "Google" searches I am still confused. Please anyone....
The problem states:
If sigma is a permutation of a set A, we say that sigma mov... |
I am truly lost as to what this problem is asking. I did post this on another forum and received what my have been wonderful advice. However, even after multiple hours and many "Google" searches I am still confused. Please anyone....
The problem states:
If $\sigma$ is a permutation of a set $A$, we say that *$\s... |
Imagine you have 36 volumes of an encyclopedia in front of you. A permutation $\sigma\in S_{36}$ is a set of instructions of how to swap positions of the volumes of that encyclopedia. For instance, the permutation $\sigma=(1,2,3,4)$ tells you to take volumes $1$ through $4$, and move volume $1$ to the second position, ... |
Imagine you have 36 volumes of an encyclopedia in front of you. A permutation $\sigma\in S_{36}$ is a set of instructions of how to swap positions of the volumes of that encyclopedia. For instance, the permutation $\sigma=(1,2,3,4)$ (this is *cycle notation*: it says element 1 is sent to element 2, element 2 is sent t... |
Question:
(a) Determine sign$(\tau)$ for $$\left( \begin{array}{ccccccc} 1&2&3&4&5&6&7 \\ 2&3&5&7&1&6&4 \end{array} \right )$$.
(b) Let $A_{n} = \{\tau \in S_{n} | \mbox{sign}(\tau) = 1\}$. Show that $A_{n}$ is a sub group of $S_{n}$ and calculate the number of elements (Tip: Show that for any transposition $\tau... |
Can anyone give a nonlinear regular function from C^2 to C^2 with a constant nonzero Jacobian? It seems to me that the only such functions are linear.
According to the Jacobian conjecture, a function from C^2 to C^2 with a constant nonzero Jacobian must have an inverse. |
With regard to combinatorics & harmonic analysis, you might find [this](http://books.google.com/books?id=qjVaD1OQbxEC&lpg=PP1&pg=PA13#v=onepage&q&f=false) interesting. [This](http://arxiv.org/PS_cache/math/pdf/0008/0008098v1.pdf) work by Terence Tao (whom you mentioned) sheds light on all three of combinatorics, analys... |
Question:
(a) Determine sign$(\tau)$ for $$\left( \begin{array}{ccccccc} 1&2&3&4&5&6&7 \\ 2&3&5&7&1&6&4 \end{array} \right )$$.
(b) Let $A_{n} = \{\tau \in S_{n} | \mbox{sign}(\tau) = 1\}$. Show that $A_{n}$ is a sub group of $S_{n}$ and calculate the number of elements (Tip: Show that for any transposition $\tau... |
Twin, cousin, and sexy primes are of the forms $(p,p+2)$, $(p,p+4)$, $(p,p+6)$ respectively, for $p$ a prime.
The Wikipedia [article on cousin primes][1] says that,
"It follows from the first Hardy–Littlewood conjecture that cousin primes have the same asymptotic density as twin primes," but the analogous [article on... |
I've just been thinking about for what values of n we can place n points in the plane so that any three of those points define an iscosceles triangle. A triangle, square and pentagon work for 3,4 and 5, and to get 6 just place a point in the centre of the pentagon.
The question is can we do this for 7 points in the ... |
Some trial and error should get it.
I figured $\left[\begin{array}{cc} x & 1\\ x-1 & 1\end{array}\right]$ was a good target Jacobian matrix, and so got $f(x,y)=(\frac 1 2 x^2 + y,\frac 1 2 x^2-x + y)$. Is that what you're looking for? Evidently it has an inverse, $g(a,b)=(a-b,a-\frac 1 2(a-b)^2)$. |
We can let $G$ act on the set of left cosets of $H$, by $g(xH) = gxH$; this is not a group, but a group action. We can also, separtely, put group structures on the set of cosets of $H$ in $G$, since it will be a set, and every nonempty set can be given a group structure (assuming the Axiom of Choice; in fact, equivalen... |
I've just been thinking about for what values of n we can place n points in the plane so that any three of those points define an isosceles triangle. A triangle, square and pentagon work for 3,4 and 5, and to get 6 just place a point in the centre of the pentagon.
The question is can we do this for 7 points in the p... |
Looking at <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069828">
the paper</a> referenced by Robin Chapman and Bill Dubuque in response to <a href="http://math.stackexchange.com/questions/14270/if-r-is-a-commutative-ring-with-identity-and-a-b-are-its-elem... |
We can let $G$ act on the set of left cosets of $H$, by $g(xH) = gxH$; this is not a group, but a group action. We can also, separtely, put group structures on the set of cosets of $H$ in $G$, since it will be a set, and every nonempty set can be given a group structure (assuming the Axiom of Choice; in fact, equivalen... |
Let $G$ be a $n \times n$ matrix with real entries and let $\Lambda = \{x^n \colon \exists i^n \in \mathbb{Z}^n \text{ such that } x^n = G \cdot i^n\}$ define a lattice. I am interested in projecting the lattice points onto a $k$-dimensional subspace $U$ with $k < n$. Let $A$ be a $n \times k$ matrix of vectors that sp... |
The problem is stated-
Do the following two sets of points have the same cardinality and if so, establish a bijection:
A line segment of length four and half of the circumference of radius one (including both endpoints).
My reasoning is they do have the same cardinality and my bijection is a picture in which I... |
Many interesting examples are in: $\ $ Barucci and Montana: [When are $\rm\ D + \frak M\ $ rings Laskerian?][1] They construct (non-Noetherian) Laskerian or strongly Laskerian rings and domains either integrally closed or not, of any dimension. They employ a frequently used powerful tool for constructing counterexampl... |
I think your lines are not vertical, right? With your construction, there are points on the semi-circle that do not have a corresponding point on the line. But you are quite close. You can 1) modify the construction so that every line from P through the semicircle hits the line (and still have every line from the li... |
I think your lines are not vertical, right? With your construction, there are points on the semi-circle that do not have a corresponding point on the line. But you are quite close. You can 1) modify the construction so that every line from P through the semicircle hits the line (and still have every line from the li... |
Given R is a ring, and b is some positive integer, prove that x + x<sup>(2b + 1)</sup> = x<sup>(2b)</sup> + x<sup>(10b + 1)</sup> is a Boolean ring, ie: x =x <sup>2</sup> for all x in R.
I am not sure where to begin with the problem, and what avenue of approach I should take such that my methodology is inclusive to... |
We can let $G$ act on the set of left cosets of $H$, by $g(xH) = gxH$; this is not a group, but a group action. We can also, separtely, put group structures on the set of cosets of $H$ in $G$, since it will be a set, and every nonempty set can be given a group structure (assuming the Axiom of Choice; in fact, equivalen... |
Given $R$ is a ring, and $b$ is some positive integer, prove that $x + x^{2b + 1} = x^{2b} + x^{10b + 1}$ is a Boolean ring, ie: $x =x^2$ for all $x$ in $R$.
I am not sure where to begin with the problem, and what avenue of approach I should take such that my methodology is inclusive to all $x$ in R.
Would it be ... |
Given $R$ is a ring, and $b$ is some positive integer such that $x + x^{2b + 1} = x^{2b} + x^{10b + 1}$ for all $x \in R$, prove that $R$ is Boolean, i.e. $x =x^2$ for all $x$ in $R$.
I am not sure where to begin with the problem, and what avenue of approach I should take such that my methodology is inclusive to al... |
By the way, your equation can be written in form
$$H^{(x)}_3=11$$
where H is the generalized harmonic number: [http://www.wolframalpha.com/input/?i=HarmonicNumber[3%2C+x]%3D%3D11][1]
So to find x you should investigate the inverse function of generalized harmonic number.
[1]: http://www.wolframalpha.co... |
Is the set of permutations in $S_{36}$ that move at most 4 elements a subgroup of $S_{36}$? |
Suppose that every interval in $\mathbb{R}$ is a connected set. Does this implies the least upper bound axiom? (i.e every non-empty subset of $\mathbb{R}$ which is bounded above has a least upper bound) Is this true? in such case, how would you prove this?
|
Does the fact that every interval in R is connected implies that R is order-complete? |
Suppose that every interval in $\mathbb{R}$ is a connected set. Does this implies the least upper bound axiom? (i.e every non-empty subset of $\mathbb{R}$ which is bounded above has a least upper bound) Is this true? in such case, how would you prove this?
|
Does the fact that every interval in $\mathbb{R}$ is connected implies that $\mathbb{R}$ is order-complete? |
Suppose that every interval in $\mathbb{R}$ is a connected set. Does this implies the least upper bound axiom? (i.e every non-empty subset of $\mathbb{R}$ which is bounded above has a least upper bound) Is this true? in such case, how would you prove this? (endowed with the usual topology)
|
Suppose that every open interval in $\mathbb{R}$ is a connected set. Does this implies the least upper bound axiom? (i.e every non-empty subset of $\mathbb{R}$ which is bounded above has a least upper bound) Is this true? in such case, how would you prove this? |
You have to show that if an element $g$ of $G$ normalises $P$, then in fact it commutes with all the elements in $P$, i.e. if the conjugation by $g$ preserves the set, then it actually preserves all the elements.
Now, if $g$ normalises $P$, then conjugation by $g$ gives you an automorphism of $P$. What is the automo... |
Let $N$ be the normalizer of $P$, and let $N$ act on $P$ by conjugation; this induces a homomorphism $N\to\mathrm{Aut}(P)$; since $P$ is abelian, it is contained in the kernel of that map, so we have that $N/P$ maps into $\mathrm{Aut}(P)$. But what is the order of the automorphism group of a cyclic group of order $p^n$... |
I'm having trouble with this integral
$$\int\arcsin(\sin(x))\,dx.$$
The problem is with the intervals of definition for each function :/ if someone could dumb it down for me.
- $\arcsin\colon [-1, 1] \to [-\pi/2, \pi/2]$.
- $\sin:\mathbb{R}\to [-1, 1]$.
right?
But what about $\arcsin(\sin x... |
I'm having trouble with this integral
$$\int\arcsin(\sin x)\,\mathrm dx$$
The problem is with the intervals of definition for each function :/ if someone could dumb it down for me.
- $\arcsin\colon [-1, 1] \to [-\pi/2, \pi/2]$.
- $\sin:\mathbb{R}\to [-1, 1]$.
right?
But what about $\arcsin(... |
Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7:
> Ford Prefect will* randomly choose
> three points on a circle. He will*
> connect these points to form a shape.
> What is the probability that the
> resulting shape will* form a right
> angled triangle?
I answered $\... |
How many right angled triangles can a circle have? |
I was talking with a friend and we were discussing a math problem disguised as a social situation:
If the chance that someone to accept your request to go out with them was 1% and you asked 1 person only, then the probability they would say yes is .01
If you were to ask 100 people, then your chances are still .01... |
Probability increases as sample size increases? |
Looking at <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069828">
the paper</a> referenced by Robin Chapman and Bill Dubuque in response to <a href="http://math.stackexchange.com/questions/14270/if-r-is-a-commutative-ring-with-identity-and-a-b-are-its-elem... |
I have the following overdetermined linear equation system:
$$Ax=b$$
where $A$ is a matrix of $n \times k$, $x$ and $b$ are vectors of $k \times 1$, where $n>k$.
We all know this is an overdetermined linear equation system.
The question is how to check whether the solution $x$ is consistent in this case? Co... |
Check Whether an Overdetermined Linear Equation System is Consistent: General Approach? |
just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with stocks having a mean of 15% and a standard deviation of 20%, and bonds having a mean of 6% and a standard devia... |
How to check if two multiplications are equal to each other or greater or lesser without actually multiplying them?
For example, compare (254)(847) and (383)(536)
EDIT:
While trying to find a rule i got one
(5)(11) < (6)(10)
or
(x)(y) < (x+1)(y-1) when y > x > 0
and another rule is that if adding... |
I have the following overdetermined linear equation system:
$$Ax=b$$
where $A$ is a matrix of $n \times k$, $x$ and $b$ are vectors of $k \times 1$, where $n>k$.
We all know this is an overdetermined linear equation system.
The question is how to check whether the solution $x$ is consistent in this case? Co... |
I have the following overdetermined linear equation system:
$$Ax=b$$
where $A$ is a matrix of $n \times k$, $x$ and $b$ are vectors of $k \times 1$, where $n>k$.
We all know this is an overdetermined linear equation system.
The question is how to check whether the solve for $x$, and check that the vector is... |
I have the following overdetermined linear equation system:
$$Ax=b$$
where $A$ is a matrix of $n \times k$, $x$ and $b$ are vectors of $k \times 1$, where $n>k$.
We all know this is an overdetermined linear equation system.
The question is how to check whether the solve for $x$, and check that the vector is... |
Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7:
> **There are 2010 points on a circle,
> evenly spaced.** Ford Prefect will*
> randomly choose three points on the
> circle. He will* connect these points
> to form a shape. What is the
> probability that the resulting sh... |
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