Invertible matrix (redirect from Inverse matrices)
invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their inverse. An n-by-n square matrix A is...
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Matrix (mathematics) (redirect from Real matrices)
In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers or other mathematical objects with elements or entries arranged in...
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established. Since for invertible matrices the pseudoinverse equals the usual inverse, only examples of non-invertible matrices are considered below. For A...
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Block matrix (redirect from Block matrices)
lines, which break it up, or partition it, into a collection of smaller matrices. For example, the 3x4 matrix presented below is divided by horizontal and...
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article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular...
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mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of...
75 KB (10,633 words) - 14:30, 26 June 2025
Orthogonal matrix (redirect from Orthogonal matrices)
own inverse, which implies that a reflection matrix is symmetric (equal to its transpose) as well as orthogonal. The product of two rotation matrices is...
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In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...
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generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized...
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product: ch. 5 or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding...
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Square matrix (redirect from Square matrice)
order n {\displaystyle n} . Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear...
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operations that are not defined for all possible operands, such as inverse matrices and inverse functions. This has been generalized to category theory, where...
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Hermitian matrix (redirect from Hermitian matrices)
Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always...
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Minor (linear algebra) (section Inverse of a matrix)
square matrices (first minors) are required for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square...
16 KB (2,729 words) - 08:42, 26 June 2025
Woodbury matrix identity (redirect from Binomial inverse theorem)
primarily used on matrices, it holds in a general ring or in an Ab-category. The Woodbury matrix identity allows cheap computation of inverses and solutions...
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Permutation matrix (redirect from Permutation matrices)
orthogonal, with its inverse equal to its transpose: P − 1 = P T {\displaystyle P^{-1}=P^{\mathsf {T}}} .: 26 Indeed, permutation matrices can be characterized...
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M-matrix (redirect from M-matrices)
non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging...
9 KB (1,180 words) - 07:28, 17 June 2025
Generalized permutation matrix (redirect from Signed permutation matrices)
the Weyl group. If a nonsingular matrix and its inverse are both nonnegative matrices (i.e. matrices with nonnegative entries), then the matrix is a generalized...
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Matrix multiplication (redirect from Multiplying matrices)
matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must...
41 KB (6,581 words) - 13:39, 28 February 2025
Hadamard matrix (redirect from Hadamard matrices)
gate "Hadamard Matrices and Designs" (PDF). UC Denver. Retrieved 11 February 2023. J.J. Sylvester. Thoughts on inverse orthogonal matrices, simultaneous...
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Rotation matrix (redirect from Rotation matrices)
"inverse" of the covering map. By properties of covering maps, the inverse can be chosen ono-to-one as a local section, but not globally. The matrices...
102 KB (15,793 words) - 07:31, 30 June 2025
Monotone matrix (redirect from Inverse-positive matrices)
matrices are M-matrices. An example is ( − 1 3 2 − 4 ) {\displaystyle \left({\begin{smallmatrix}-1&3\\2&-4\end{smallmatrix}}\right)} , whose inverse is...
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1 ( b ) , J f ( a ) {\displaystyle Jf^{-1}(b),Jf(a)} are the Jacobian matrices representing ( f − 1 ) ′ ( b ) , f ′ ( a ) {\displaystyle (f^{-1})'(b)...
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Identity matrix (redirect from Identity matrices)
equal to its own inverse. In this group, two square matrices have the identity matrix as their product exactly when they are the inverses of each other....
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Logarithm of a matrix (category Inverse functions)
logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may...
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Definite matrix (redirect from Positive-definite matrices)
transpose of z . {\displaystyle \mathbf {z} .} Positive semi-definite matrices are defined similarly, except that the scalars x T M x {\displaystyle \mathbf...
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satisfactory. The inverse iteration algorithm requires solving a linear system or calculation of the inverse matrix. For non-structured matrices (not sparse...
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trigonometric functions (especially sine and cosine) for complex square matrices occur in solutions of second-order systems of differential equations. They...
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the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I). The name given to...
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Integer matrix (redirect from Integral matrices)
integers. Examples include binary matrices, the zero matrix, the matrix of ones, the identity matrix, and the adjacency matrices used in graph theory, amongst...
3 KB (411 words) - 15:50, 24 June 2025