(multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity...
46 KB (6,940 words) - 00:07, 6 July 2024
and in particular linear algebra, the Moore–Penrose inverse A + {\displaystyle A^{+}} of a matrix A {\displaystyle A} , often called the pseudoinverse...
46 KB (7,504 words) - 07:26, 31 August 2024
{\displaystyle n\times n} identity matrix. The matrix Ω {\displaystyle \Omega } has determinant + 1 {\displaystyle +1} and its inverse is Ω − 1 = Ω T = − Ω {\displaystyle...
15 KB (2,322 words) - 09:09, 14 August 2024
algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing...
17 KB (2,090 words) - 16:00, 11 September 2024
unknowns are different so that matrix F {\displaystyle F} is not square. However, even a square matrix can have no inverse: matrix F {\displaystyle F} can be...
66 KB (8,990 words) - 19:54, 11 September 2024
to the identity matrix I {\displaystyle \mathbf {I} } , the right-hand n × n {\displaystyle n\times n} block is then the inverse matrix A − 1 {\displaystyle...
7 KB (1,310 words) - 20:10, 15 May 2024
Sherman–Morrison formula (category Matrix theory)
computes the inverse of a "rank-1 update" to a matrix whose inverse has previously been computed. That is, given an invertible matrix A {\displaystyle...
10 KB (1,802 words) - 14:26, 27 August 2024
may be satisfactory. The inverse iteration algorithm requires solving a linear system or calculation of the inverse matrix. For non-structured matrices...
12 KB (2,055 words) - 04:26, 30 November 2023
Inverse element Inverse function, a function that "reverses" another function Generalized inverse, a matrix that has some properties of the inverse matrix...
1 KB (176 words) - 02:15, 22 June 2021
where A−1 is the inverse matrix of A. If A has no inverse, solutions—if any—can be found using its generalized inverse. Matrices and matrix multiplication...
106 KB (13,087 words) - 06:38, 15 September 2024
entries), an invertible matrix is a matrix that has an inverse that is also an integer matrix. Such a matrix is called a unimodular matrix for distinguishing...
30 KB (4,478 words) - 07:43, 4 July 2024
Q^{\mathrm {T} }=Q^{-1},} where Q−1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where...
36 KB (4,802 words) - 16:45, 22 May 2024
Cramer's rule (section Finding inverse matrix)
left inverse of a square matrix is also a right-inverse (see Invertible matrix theorem). For other proofs, see below. Let A be an n × n matrix with entries...
28 KB (4,029 words) - 15:20, 18 June 2024
multiplicative inverse. For example, a matrix such that all entries of a row (or a column) are 0 does not have an inverse. If it exists, the inverse of a matrix A...
41 KB (6,581 words) - 00:29, 9 September 2024
corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an...
32 KB (4,252 words) - 22:13, 9 September 2024
In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. It is a more...
3 KB (152 words) - 20:36, 15 April 2024
formulas for the inverse matrix V − 1 {\displaystyle V^{-1}} . In particular, Lagrange interpolation shows that the columns of the inverse matrix V − 1 = [ 1...
21 KB (4,611 words) - 08:02, 9 September 2024
algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors...
40 KB (5,589 words) - 01:55, 2 September 2024
is unique and is called the inverse matrix of A {\displaystyle A} , denoted A − 1 {\displaystyle A^{-1}} . A square matrix A {\displaystyle A} that is...
16 KB (1,831 words) - 06:07, 16 June 2024
The purpose of constructing a 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...
15 KB (2,592 words) - 12:57, 5 September 2024
advanced linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗...
10 KB (1,308 words) - 07:48, 31 August 2024
Transpose (redirect from Transpose of a matrix)
transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original matrix. The notation A−T is sometimes...
20 KB (2,525 words) - 12:30, 8 May 2024
,} where I is the identity matrix of the same size as A. Consequently, the multiplicative inverse of an invertible matrix can be found by dividing its...
29 KB (4,813 words) - 16:24, 22 May 2024
prior for the covariance matrix of a multivariate normal distribution. We say X {\displaystyle \mathbf {X} } follows an inverse Wishart distribution, denoted...
20 KB (3,472 words) - 23:35, 14 May 2024
Other inverse distributions include inverse-chi-squared distribution inverse-gamma distribution inverse-Wishart distribution inverse matrix gamma distribution...
12 KB (1,718 words) - 19:51, 11 September 2024
In mathematics, an involutory matrix is a square matrix that is its own inverse. That is, multiplication by the matrix A n × n {\displaystyle A_{n\times...
7 KB (925 words) - 08:30, 16 September 2024
Minor (linear algebra) (redirect from Minor (matrix theory))
matrix cofactors, which in turn are useful for computing both the determinant and inverse of square matrices. The requirement that the square matrix be...
15 KB (2,716 words) - 15:52, 1 November 2023
its domain, giving a formula for the Jacobian matrix of the inverse. There are also versions of the inverse function theorem for holomorphic functions,...
39 KB (7,303 words) - 00:11, 8 August 2024
In linear algebra and statistics, the partial inverse of a matrix is an operation related to Gaussian elimination which has applications in numerical...
4 KB (691 words) - 08:55, 17 November 2022
post-multiplying an n-column matrix M, forming MP, permutes the columns of M. Every permutation matrix P is orthogonal, with its inverse equal to its transpose:...
18 KB (3,042 words) - 07:31, 27 August 2024