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Spectral theorem Summary Spectral_theorem In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral theorem Summary Spectral_theorem In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral theorem Summary Spectral_theorem Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral theorem also provides a canonical decomposition, called the spectral decomposition, of the underlying vector space on which ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral theorem Summary Spectral_theorem In addition, Cauchy was the first to be systematic about determinants. The spectral theorem as generalized by John von Neumann is today perhaps the most important result of operator theory. This article mainly focuses on the simplest kind of spectral theorem, that for a self-ad... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gram-Schmidt theorem Summary Gram–Schmidt_decomposition In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inne... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zero tensor Zero matrix Zero_vector > Zero matrix In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. It is alternately denoted by the symbol O {\displaystyle O} . Some examples of zero matrices are 0 1 , 1 = , 0 2 , 2 = , 0 2 , 3 = , {\displaystyle 0_{1,1}={\begin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zero tensor Zero matrix Zero_vector > Zero matrix 0 K m , n = {\displaystyle 0_{K_{m,n}}={\begin{bmatrix}0_{K}&0_{K}&\cdots &0_{K}\\0_{K}&0_{K}&\cdots &0_{K}\\\vdots &\vdots &&\vdots \\0_{K}&0_{K}&\cdots &0_{K}\end{bmatrix}}} The zero matrix is the additive identity in K m , n {\displaystyle K_{m,n}} . That is, for al... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zero tensor Zero matrix Zero_vector > Zero matrix In general, the zero element of a ring is unique, and typically denoted as 0 without any subscript to indicate the parent ring. Hence the examples above represent zero matrices over any ring. The zero matrix also represents the linear transformation which sends all vect... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zero matrix Summary Mortal_matrix_problem In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of m × n {\displaystyle m\times n} matrices, and is denoted by the symbol O {\displaystyle O} or 0 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Orthogonal basis Summary Orthogonal_basis In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V {\displaystyle V} is a basis for V {\displaystyle V} whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V {\displaystyle V} whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For exampl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system {\displaystyle V.} Under these coordinates, the inner product becomes a dot product of vectors. Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of R n {\displaystyle \mathbb {R} ^{n}} under... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system Every finite-dimensional inner product space has an orthonormal basis, which may be obtained from an arbitrary basis using the Gram–Schmidt process. In functional analysis, the concept of an orthonormal basis can be generalized to arbitrary (infinite-dimensi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system In this case, the orthonormal basis is sometimes called a Hilbert basis for H . {\displaystyle H.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system Note that an orthonormal basis in this sense is not generally a Hamel basis, since infinite linear combinations are required. Specifically, the linear span of the basis must be dense in H , {\displaystyle H,} but it may not be the entire space. If we go on t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete orthonormal basis Summary Complete_orthogonal_system For instance, any square-integrable function on the interval {\displaystyle } can be expressed (almost everywhere) as an infinite sum of Legendre polynomials (an orthonormal basis), but not necessarily as an infinite sum of the monomials x n . {\displaystyl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Schur–Horn theorem Summary Schur–Horn_theorem In mathematics, particularly linear algebra, the Schur–Horn theorem, named after Issai Schur and Alfred Horn, characterizes the diagonal of a Hermitian matrix with given eigenvalues. It has inspired investigations and substantial generalizations in the setting of symplectic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pascal matrix Summary Pascal_matrix In mathematics, particularly matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an encoding of Pascal's triangle in matrix form. There are three natural ways to achieve this: as a lower-tri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stieltjes matrix Summary Stieltjes_matrix In mathematics, particularly matrix theory, a Stieltjes matrix, named after Thomas Joannes Stieltjes, is a real symmetric positive definite matrix with nonpositive off-diagonal entries. A Stieltjes matrix is necessarily an M-matrix. Every n×n Stieltjes matrix is invertible to a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bandwidth (linear algebra) Summary Band_matrix In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lehmer matrix Summary Lehmer_matrix In mathematics, particularly matrix theory, the n×n Lehmer matrix (named after Derrick Henry Lehmer) is the constant symmetric matrix defined by A i j = { i / j , j ≥ i j / i , j < i . {\displaystyle A_{ij}={\begin{cases}i/j,&j\geq i\\j/i,&j | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ideal Summary Sigma-ideal In mathematics, particularly measure theory, a 𝜎-ideal, or sigma ideal, of a sigma-algebra (𝜎, read "sigma," means countable in this context) is a subset with certain desirable closure properties. It is a special type of ideal. Its most frequent application is in probability theory.Let... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ideal Summary Sigma-ideal {\textstyle \bigcup _{n\in \mathbb {N} }A_{n}\in N.} Briefly, a sigma-ideal must contain the empty set and contain subsets and countable unions of its elements. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ideal Summary Sigma-ideal The concept of 𝜎-ideal is dual to that of a countably complete (𝜎-) filter. If a measure μ {\displaystyle \mu } is given on ( X , Σ ) , {\displaystyle (X,\Sigma ),} the set of μ {\displaystyle \mu } -negligible sets ( S ∈ Σ {\displaystyle S\in \Sigma } such that μ ( S ) = 0 {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ideal Summary Sigma-ideal {\displaystyle y.} Thus I {\displaystyle I} contains the bottom element, is downward closed, and satisfies a countable analogue of the property of being upwards directed. A 𝜎-ideal of a set X {\displaystyle X} is a 𝜎-ideal of the power set of X . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ideal Summary Sigma-ideal {\displaystyle X.} That is, when no 𝜎-algebra is specified, then one simply takes the full power set of the underlying set. For example, the meager subsets of a topological space are those in the 𝜎-ideal generated by the collection of closed subsets with empty interior. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Surface integral Summary Surface_integral In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bramble–Hilbert lemma Summary Bramble–Hilbert_lemma In mathematics, particularly numerical analysis, the Bramble–Hilbert lemma, named after James H. Bramble and Stephen Hilbert, bounds the error of an approximation of a function u {\displaystyle \textstyle u} by a polynomial of order at most m − 1 {\displaystyle \texts... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bramble–Hilbert lemma Summary Bramble–Hilbert_lemma Additional assumptions on the domain are needed for the Bramble–Hilbert lemma to hold. Essentially, the boundary of the domain must be "reasonable". For example, domains that have a spike or a slit with zero angle at the tip are excluded. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bramble–Hilbert lemma Summary Bramble–Hilbert_lemma Lipschitz domains are reasonable enough, which includes convex domains and domains with continuously differentiable boundary. The main use of the Bramble–Hilbert lemma is to prove bounds on the error of interpolation of function u {\displaystyle \textstyle u} by an op... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic exponential function Summary P-adic_logarithm In mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function, named the p-adic logarithm. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ramanujan theta function Summary Ramanujan_theta_function In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tarski finiteness Summary Tarski_finiteness In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, { 2 , 4 , 6 , 8 , 10 } {\displaystyle \{2,4,6,8,10\}} is a finite set wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tarski finiteness Summary Tarski_finiteness A set that is not a finite set is called an infinite set. For example, the set of all positive integers is infinite: { 1 , 2 , 3 , … } . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tarski finiteness Summary Tarski_finiteness {\displaystyle \{1,2,3,\ldots \}.} Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger fini... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonrecursive ordinals Summary Nonrecursive_ordinals In mathematics, particularly set theory, non-recursive ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using recursive ordinal notations. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Simple homotopy Summary Simple_homotopy_type In mathematics, particularly the area of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence. Two CW-complexes are simple-homotopy equivalent if they are related by a sequence of collapses and expansions (inverses of collapses), and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
2-group Summary 2-group In mathematics, particularly the branch called category theory, a 2-group is a groupoid with a way to multiply objects, making it resemble a group. They are part of a larger hierarchy of n-groups. They were introduced by Hoàng Xuân Sính in the late 1960s under the name gr-categories, and they ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fourier cosine series Summary Cosine_series In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dunkl operator Summary Dunkl_operator In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space. Formally, let G be a Coxeter group with reduced root system R and kv an arbitrary "multip... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dunkl operator Summary Dunkl_operator Dunkl operators were introduced by Charles Dunkl (1989). One of Dunkl's major results was that Dunkl operators "commute," that is, they satisfy T i ( T j f ( x ) ) = T j ( T i f ( x ) ) {\displaystyle T_{i}(T_{j}f(x))=T_{j}(T_{i}f(x))} just as partial derivatives do. Thus Dunkl ope... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
G-delta space Summary G-delta_space In mathematics, particularly topology, a Gδ space is a topological space in which closed sets are in a way ‘separated’ from their complements using only countably many open sets. A Gδ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact norma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Comb space Summary Comb_space In mathematics, particularly topology, a comb space is a particular subspace of R 2 {\displaystyle \mathbb {R} ^{2}} that resembles a comb. The comb space has properties that serve as a number of counterexamples. The topologist's sine curve has similar properties to the comb space. The del... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cosmic space Summary Cosmic_space In mathematics, particularly topology, a cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular T1 spaces but not in general), a space is cosmic if and only if it has a countable network; namely a countable collection ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally normal space Summary Locally_normal_space In mathematics, particularly topology, a topological space X is locally normal if intuitively it looks locally like a normal space. More precisely, a locally normal space satisfies the property that each point of the space belongs to a neighbourhood of the space that is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coordinate map Summary Local_coordinate_system In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. If the manifold is the surface of the Earth, then an atlas has its more com... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally discrete collection Summary Locally_discrete_collection In mathematics, particularly topology, collections of subsets are said to be locally discrete if they look like they have precisely one element from a local point of view. The study of locally discrete collections is worthwhile as Bing's metrization theore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
K-topology Summary K-topology In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n | n is a positive integer} is not closed si... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homeomorphism group Summary Homeomorphism_group In mathematics, particularly topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function composition as the group operation. Homeomorphism groups are very important in the theory of topologi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tube lemma Summary Tube_lemma In mathematics, particularly topology, the tube lemma, also called Wallace's theorem, is a useful tool in order to prove that the finite product of compact spaces is compact. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleman's condition Summary Carleman's_condition In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure μ {\displaystyle \mu } satisfies Carleman's condition, there is no other measure ν {\displaystyle \nu } having t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Milman's reverse Brunn–Minkowski inequality Summary Milman's_reverse_Brunn–Minkowski_inequality In mathematics, particularly, in asymptotic convex geometry, Milman's reverse Brunn–Minkowski inequality is a result due to Vitali Milman that provides a reverse inequality to the famous Brunn–Minkowski inequality for convex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pentation Summary Pentation In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity), just as tetration is iterated right-associative exponentiation. It is a binary operation defined with two numb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perfectoid space Summary Perfectoid_field In mathematics, perfectoid spaces are adic spaces of special kind, which occur in the study of problems of "mixed characteristic", such as local fields of characteristic zero which have residue fields of characteristic prime p. A perfectoid field is a complete topological field... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Persymmetric matrix Summary Persymmetric_matrix In mathematics, persymmetric matrix may refer to: a square matrix which is symmetric with respect to the northeast-to-southwest diagonal; or a square matrix such that the values on each line perpendicular to the main diagonal are the same for a given line.The first defini... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perturbation problem beyond all orders Summary Perturbation_problem_beyond_all_orders In mathematics, perturbation theory works typically by expanding unknown quantity in a power series in a small parameter. However, in a perturbation problem beyond all orders, all coefficients of the perturbation expansion vanish and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perturbation problem beyond all orders Summary Perturbation_problem_beyond_all_orders This is because the function e − 1 / z {\displaystyle e^{-1/z}} possesses an essential singularity at z = 0 {\displaystyle z=0} in the complex z {\displaystyle z} -plane, and therefore the function is most appropriately modeled by a L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Space groups Summary Space_group In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, spa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Space groups Summary Space_group In dimensions other than 3, they are sometimes called Bieberbach groups. In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the I... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sinc function Summary Unnormalized_sinc_function In mathematics, physics and engineering, the sinc function, denoted by sinc(x), has two forms, normalized and unnormalized. In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by Alternatively, the unnormalized sinc function is often called the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sinc function Summary Unnormalized_sinc_function It is used in the concept of reconstructing a continuous bandlimited signal from uniformly spaced samples of that signal. The only difference between the two definitions is in the scaling of the independent variable (the x axis) by a factor of π. In both cases, the value... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sinc function Summary Unnormalized_sinc_function The sinc function is then analytic everywhere and hence an entire function. The function has also been called the cardinal sine or sine cardinal function. The term sinc was introduced by Philip M. Woodward in his 1952 article "Information theory and inverse probability i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moiré effect Summary Moire_pattern In mathematics, physics, and art, moiré patterns (UK: MWAR-ay, US: mwar-AY, French: ) or moiré fringes are large-scale interference patterns that can be produced when a partially opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré interfer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moiré effect Summary Moire_pattern In television and digital photography, a pattern on an object being photographed can interfere with the shape of the light sensors to generate unwanted artifacts. They are also sometimes created deliberately – in micrometers they are used to amplify the effects of very small movements... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Introduction to the mathematics of general relativity Vectors Introduction_to_the_mathematics_of_general_relativity > Vectors and tensors > Vectors In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or – as here – simply a vector) is a geometric object that has... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector direction Summary Resultant_vector In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Eucli... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector direction Summary Resultant_vector It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector direction Summary Resultant_vector Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (exc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spatial frequency Summary Spatial_frequencies In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier transform) of the structure repeat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spatial frequency Summary Spatial_frequencies In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter (mm) or equivalently line pairs per mm. In wave propagation, the spatial frequency is also known as wavenumber. Ordinary wavenumber is defined as the reciprocal of wavel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tapering (mathematics) Summary Tapering_(mathematics) In mathematics, physics, and theoretical computer graphics, tapering is a kind of shape deformation. Just as an affine transformation, such as scaling or shearing, is a first-order model of shape deformation, tapering is a higher order deformation just as twisting a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tapering (mathematics) Summary Tapering_(mathematics) To create a nonlinear taper, instead of scaling in x and y for all z with constants as in: q = p , {\displaystyle q={\begin{bmatrix}a&0&0\\0&b&0\\0&0&1\end{bmatrix}}p,} let a and b be functions of z so that: q = p . {\displaystyle q={\begin{bmatrix}a(p_{z})&0&0\\0... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frequency space Summary Frequency_component In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over tim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frequency space Summary Frequency_component Although it is common to refer to the magnitude portion as the frequency response of a signal, the phase portion is required to uniquely define the signal. A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frequency space Summary Frequency_component The "spectrum" of frequency components is the frequency-domain representation of the signal. The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum analyzer is a tool commonly used to visualize electronic signals in t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frequency space Summary Frequency_component A frequency-domain representation may describe either a static function or a particular time period of a dynamic function (signal or system). The frequency transform of a dynamic function is performed over a finite time period of that function and assumes the function repeats... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Piecewise syndetic set Summary Piecewise_syndetic_set In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. A set S ⊂ N {\displaystyle S\subset \mathbb {N} } is called piecewise syndetic if there exists a finite subset G of N {\displaystyle \mathbb {N} } such that for every f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Planar algebra Summary Planar_algebra In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the propert... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Plurisubharmonic function Summary Plurisubharmonic_function In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. Howe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Point-free geometry Summary Whitehead's_point-free_geometry In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory. Point-free geometry... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pointless topology Summary Pointless_topology In mathematics, pointless topology, also called point-free topology (or pointfree topology) and locale theory, is an approach to topology that avoids mentioning points, and in which the lattices of open sets are the primitive notions. In this approach it becomes possible to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topology of pointwise convergence Summary Pointwise_convergence In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number In mathematics, poly-Bernoulli numbers, denoted as B n ( k ) {\displaystyle B_{n}^{(k)}} , were defined by M. Kaneko as L i k ( 1 − e − x ) 1 − e − x = ∑ n = 0 ∞ B n ( k ) x n n ! {\displaystyle {Li_{k}(1-e^{-x}) \over 1-e^{-x}}=\sum _{n=0}^{\infty }B_{n}^{(k)}{x^{n} ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined as follows L i k ( 1 − ( a b ) − x ) b x − a − x c x t = ∑ n = 0 ∞ B n ( k ) ( t ; a , b , c ) x n n ! {\displaystyle {Li_{k}(1-(ab)^{-x}) \over b^{x}-a^{-x}}c^{xt}=\sum _{n=0}^{\inft... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number where Li is the polylogarithm. Kaneko also gave two combinatorial formulas: B n ( − k ) = ∑ m = 0 n ( − 1 ) m + n m ! S ( n , m ) ( m + 1 ) k , {\displaystyle B_{n}^{(-k)}=\sum _{m=0}^{n}(-1)^{m+n}m!S(n,m)(m+1)^{k},} B n ( − k ) = ∑ j = 0 min ( n , k ) ( j ! ) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number 2 S ( n + 1 , j + 1 ) S ( k + 1 , j + 1 ) , {\displaystyle B_{n}^{(-k)}=\sum _{j=0}^{\min(n,k)}(j! )^{2}S(n+1,j+1)S(k+1,j+1),} where S ( n , k ) {\displaystyle S(n,k)} is the number of ways to partition a size n {\displaystyle n} set into k {\displaystyle k} non-empty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number Also it is the number of open tours by a biased rook on a board 1 ⋯ 1 ⏟ n 0 ⋯ 0 ⏟ k {\displaystyle \underbrace {1\cdots 1} _{n}\underbrace {0\cdots 0} _{k}} (see A329718 for definition). The Poly-Bernoulli number B k ( − k ) {\displaystyle B_{k}^{(-k)}} satisfies the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poly-Bernoulli number Summary Poly-Bernoulli_number {\displaystyle B_{k}^{(-k)}\sim (k! )^{2}{\sqrt {\frac {1}{k\pi (1-\log 2)}}}\left({\frac {1}{\log 2}}\right)^{2k+1},\quad {\text{as }}k\rightarrow \infty .} For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfy B n ( − p ) ≡ 2 n ( mod p ) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polyad Summary Polyad In mathematics, polyad is a concept of category theory introduced by Jean Bénabou in generalising monads. A polyad in a bicategory D is a bicategory morphism Φ from a locally punctual bicategory C to D, Φ: C → D. (A bicategory C is called locally punctual if all hom-categories C(X,Y) consist of on... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial identity testing Summary Polynomial_identity_testing In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decid... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive definite Summary Positive_definiteness In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular: Positive-definite bilinear form Positive-definite function Positive-definite func... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Potential flow around a circular cylinder Summary Potential_flow_around_a_circular_cylinder In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Power method Summary Power_iteration In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\displaystyle A} , the algorithm will produce a number λ {\displaystyle \lambda } , which is the greatest (in absolute value) eigenvalue of A {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pluriharmonic function Summary Pluriharmonic_function In mathematics, precisely in the theory of functions of several complex variables, a pluriharmonic function is a real valued function which is locally the real part of a holomorphic function of several complex variables. Sometimes such a function is referred to as n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primitive recursive ordinal function Summary Primitive_recursive_ordinal_function In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They were introduced by Jensen & Karp (1971... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Probabilistic metric space Summary Probabilistic_metric_space In mathematics, probabilistic metric spaces are a generalization of metric spaces where the distance no longer takes values in the non-negative real numbers R ≥ 0, but in distribution functions.Let D+ be the set of all probability distribution functions F su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Progressively measurable Summary Progressively_measurable_process In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively mea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Projections onto convex sets Summary Projections_onto_convex_sets In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simple algorithm and has been rediscovered many times. The ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Projections onto convex sets Summary Projections_onto_convex_sets For general closed convex sets, the limit point need not be the projection. Classical work on the case of two closed convex sets shows that the rate of convergence of the iterates is linear. There are now extensions that consider cases when there are mor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Projections onto convex sets Summary Projections_onto_convex_sets Analysis of POCS and related methods attempt to show that the algorithm converges (and if so, find the rate of convergence), and whether it converges to the projection of the original point. These questions are largely known for simple cases, but a topic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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