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- ...or equivalently if their [[commutator]] <math>[A,B]= AB-BA</math> is zero. Matrices <math>A</math> that commute with matrix <math>B</math> are called the '''co ...said to '''commute''' if they commute pairwise, meaning that every pair of matrices in the set commutes. ...9 KB (1,414 words) - 20:47, 24 December 2024
- ...is an {{nobr|(''N'' + 1) × (''N'' + 1)}} matrix. The first few Krawtchouk matrices are: ...Feinsilver |first1=P. |last2=Kocik |first2=J. |date=2007 |title=Krawtchouk matrices from classical and quantum random walks |eprint=quant-ph/0702173}}</ref> ...4 KB (510 words) - 19:47, 12 August 2023
- {{Short description|Elementwise product of two matrices}} ...product qtl1.svg|thumb|The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions.]] ...21 KB (2,994 words) - 14:53, 7 January 2025
- {{Short description|Basic definition and properties of the category of matrices}} ...are [[natural number]]s and whose [[morphism]]s are [[matrix (mathematics)|matrices]], with composition given by [[matrix multiplication]].<ref>{{harvp|Riehl|2 ...6 KB (923 words) - 16:13, 30 June 2024
- {{Short description|Gamma matrices for arbitrary Clifford algebras}} ...struction of higher-dimensional gamma matrices for [[Weyl spinor]]s. Gamma matrices also appear in generic settings in [[Riemannian geometry]], particularly wh ...25 KB (3,764 words) - 04:00, 28 October 2024
- ...s of [[complex numbers]]:<ref name="Higham">{{cite book|title=Functions of matrices: theory and computation|author=Nicholas J. Higham|year=2008|pages=287f|isbn For example, taking {{mvar|X}} to be a standard [[Pauli matrices|Pauli matrix]], ...4 KB (563 words) - 13:50, 5 August 2024
- In mathematics, the '''Jacobi method for complex [[Hermitian matrices]]''' is a generalization of the [[Jacobi eigenvalue algorithm|Jacobi iterat ...or [[Jacobi eigenvalue algorithm|Jacobi iteration]] of complex [[Hermitian matrices]] in order to find a numerical estimation of their eigenvectors and eigenva ...5 KB (858 words) - 08:52, 15 July 2015
- '''Joint Approximation Diagonalization of Eigen-matrices (JADE)''' is an algorithm for [[independent component analysis]] that separ ...2 KB (337 words) - 22:27, 25 January 2024
Page text matches
- ...]], [[tridiagonal matrix|tridiagonal]], order-''N'' [[matrix (mathematics)|matrices]] with pairs of nearly, but not exactly, equal [[eigenvalue]]s.<ref>{{cite Wilkinson matrices have applications in many fields, including [[scientific computing]], [[num ...1 KB (109 words) - 19:28, 12 August 2023
- ...''n'' matrices. That such polynomials exist for any [[Square matrix|square matrices]] was discovered in 1970 independently by [[Edward W. Formanek|Formanek]] a ...]], one has that <math>(xy - yx)^2 = -\det(xy - yx)I</math> for any 2-by-2-matrices ''x'' and ''y''. ...1 KB (209 words) - 06:58, 13 May 2024
- ==Applied to matrices== Two [[matrix (mathematics)|matrices]] <math>p</math> and <math>q</math> are said to have the [[commutative prop ...2 KB (372 words) - 05:21, 5 July 2023
- ...[[mathematics]], the class of L-matrices are those [[matrix (mathematics)|matrices]] whose off-diagonal entries are less than or equal to zero and whose diago [[Category:Matrices]] ...955 bytes (129 words) - 13:02, 2 October 2023
- ...ained by complementing each element. The intersection or union of two such matrices is obtained by applying the operation to entries of each pair of elements t The product of two Boolean matrices is expressed as follows: ...3 KB (427 words) - 07:58, 31 May 2024
- ...atorial matrix theory]] the '''Williamson conjecture''' is that Williamson matrices of order <math>n</math> exist for all positive integers <math>n</math>. ..., <math>B</math>, <math>C</math>, <math>D</math> are known as ''Williamson matrices'' if their entries are <math>\pm1</math> and they satisfy the relationship ...3 KB (376 words) - 16:11, 16 January 2025
- In [[linear algebra]], two ''n''-by-''n'' [[matrix (mathematics)|matrices]] ''A'' and ''B'' are called '''consimilar''' if ...bar{S}</math> denotes the elementwise [[complex conjugation]]. So for real matrices similar by some real matrix <math>S</math>, consimilarity is the same as [[ ...2 KB (239 words) - 19:33, 12 August 2023
- ...Thus, EP matrices are also known as RPN (Range Perpendicular to Nullspace) matrices. ...lgebra)|Projectors]]'' instead, since an equivalent characterization of EP matrices is based in terms of equality of the projectors ''AA<sup>+</sup>'' and ''A< ...4 KB (636 words) - 18:51, 31 March 2021
- ...ite journal|last1=Mangasarian|first1=O. L.|title=Characterizations of Real Matrices of Monotone Kind|journal=SIAM Review|volume=10|issue=4|year=1968|pages=439– Note, however, that not all monotone matrices are M-matrices. An example is <math>\left( \begin{smallmatrix} -1&3\\ 2&-4 \end{smallmatri ...2 KB (341 words) - 09:58, 11 May 2024
- ...M(R)</math> is its [[ideal (ring theory)|ideal]] of [[matrix (mathematics)|matrices]] having only finitely many nonzero elements. It is an analog of [[suspensi ...918 bytes (138 words) - 06:43, 13 May 2024
- **[[Kronecker product]], the tensor product of matrices (or vectors), which satisfies all the properties for vector spaces and allo ...djacency matrices are the [[Kronecker product]] of the component adjacency matrices ...2 KB (256 words) - 17:01, 22 May 2023
- The [[symplectic group]] Sp<sub>2''g''</sub>('''Z''') consists of the matrices ...oup Γ<sub>g</sub>(''n'',2''n'') = Γ<sub>''n'',2''n''</sub> consists of the matrices ...1 KB (219 words) - 01:36, 3 October 2017
- {{Short description|Basic definition and properties of the category of matrices}} ...are [[natural number]]s and whose [[morphism]]s are [[matrix (mathematics)|matrices]], with composition given by [[matrix multiplication]].<ref>{{harvp|Riehl|2 ...6 KB (923 words) - 16:13, 30 June 2024
- {{Short description|Binary operation, takes two matrices and returns a scalar}} ...er of rows and columns—but are not restricted to be [[square matrix|square matrices]]. ...6 KB (912 words) - 03:51, 27 February 2025
- ...olume=281|issue=1–3|date=15 September 1998|pages=87–96|title=On Nekrasov's matrices|quotation=See definition 2.1|doi=10.1016/S0024-3795(98)10031-9|last1=Li|fir [[Category:Matrices]] ...909 bytes (131 words) - 11:51, 23 June 2024
- ...is an {{nobr|(''N'' + 1) × (''N'' + 1)}} matrix. The first few Krawtchouk matrices are: ...Feinsilver |first1=P. |last2=Kocik |first2=J. |date=2007 |title=Krawtchouk matrices from classical and quantum random walks |eprint=quant-ph/0702173}}</ref> ...4 KB (510 words) - 19:47, 12 August 2023
- In mathematics, the '''Jacobi method for complex [[Hermitian matrices]]''' is a generalization of the [[Jacobi eigenvalue algorithm|Jacobi iterat ...or [[Jacobi eigenvalue algorithm|Jacobi iteration]] of complex [[Hermitian matrices]] in order to find a numerical estimation of their eigenvectors and eigenva ...5 KB (858 words) - 08:52, 15 July 2015
- ...-7|issn=0002-9947|doi-access=free}}</ref> Given the polynomial ''p'', the matrices ''A'' and ''B'' can be found by elementary methods.<ref>{{Citation|last1=Cr ...2 KB (240 words) - 03:43, 21 August 2024
- {{short description|Theorem about diagonalizing matrices}} ...matrix|positive definite matrices]] through [[Symplectic matrix|symplectic matrices]].<ref>{{Cite journal |last=Williamson |first=John |date=1936 |title=On the ...3 KB (468 words) - 02:16, 31 January 2025
- {{Short description|Algebra of complex square matrices}} ...atrix multiplication|ordinary matrix multiplication]], [[Hadamard product (matrices)|Schur product]], [[Matrix transpose|transposition]], and contains both the ...5 KB (878 words) - 23:53, 3 May 2024