• 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...
    46 KB (7,049 words) - 17:28, 22 June 2025
  • Thumbnail for Matrix (mathematics)
    In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers or other mathematical objects with elements or entries arranged in...
    122 KB (14,767 words) - 21:12, 1 July 2025
  • established. Since for invertible matrices the pseudoinverse equals the usual inverse, only examples of non-invertible matrices are considered below. For A...
    47 KB (7,644 words) - 15:31, 24 June 2025
  • Thumbnail for Block matrix
    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...
    31 KB (5,122 words) - 03:49, 2 June 2025
  • Thumbnail for List of named matrices
    article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular...
    32 KB (1,336 words) - 21:01, 14 April 2025
  • Thumbnail for Inverse trigonometric functions
    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
  • 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...
    36 KB (4,802 words) - 21:06, 14 April 2025
  • Thumbnail for Pauli matrices
    In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...
    45 KB (7,495 words) - 12:51, 23 May 2025
  • 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...
    15 KB (2,592 words) - 21:04, 14 April 2025
  • Thumbnail for Hadamard product (matrices)
    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...
    21 KB (2,762 words) - 17:37, 18 June 2025
  • Thumbnail for Square matrix
    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...
    16 KB (1,834 words) - 21:01, 14 April 2025
  • operations that are not defined for all possible operands, such as inverse matrices and inverse functions. This has been generalized to category theory, where...
    30 KB (4,478 words) - 08:38, 30 June 2025
  • 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...
    20 KB (3,028 words) - 01:11, 26 May 2025
  • 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
  • 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...
    17 KB (2,090 words) - 21:09, 14 April 2025
  • 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...
    18 KB (3,047 words) - 21:06, 14 April 2025
  • 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
  • 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...
    6 KB (899 words) - 21:04, 14 April 2025
  • Thumbnail for Matrix multiplication
    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
  • Thumbnail for Hadamard matrix
    gate "Hadamard Matrices and Designs" (PDF). UC Denver. Retrieved 11 February 2023. J.J. Sylvester. Thoughts on inverse orthogonal matrices, simultaneous...
    26 KB (3,716 words) - 20:33, 18 May 2025
  • "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
  • 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...
    2 KB (377 words) - 07:28, 17 June 2025
  • 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)...
    42 KB (7,930 words) - 16:02, 27 May 2025
  • 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....
    6 KB (841 words) - 21:05, 14 April 2025
  • 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...
    18 KB (2,982 words) - 14:00, 26 May 2025
  • transpose of z . {\displaystyle \mathbf {z} .} Positive semi-definite matrices are defined similarly, except that the scalars x T M x {\displaystyle \mathbf...
    50 KB (8,817 words) - 17:28, 20 May 2025
  • satisfactory. The inverse iteration algorithm requires solving a linear system or calculation of the inverse matrix. For non-structured matrices (not sparse...
    12 KB (2,055 words) - 19:03, 3 June 2025
  • trigonometric functions (especially sine and cosine) for complex square matrices occur in solutions of second-order systems of differential equations. They...
    4 KB (601 words) - 12:50, 5 August 2024
  • Thumbnail for Inverse distance weighting
    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...
    10 KB (1,383 words) - 17:23, 23 June 2025
  • 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