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Invertible matrix. In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. Invertible matrices are the same size as their inverse.
Moore–Penrose inverse. In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [1] It was independently described by E. H. Moore in 1920, [2] Arne Bjerhammar in 1951, [3] and Roger Penrose in 1955. [4]
In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury [1][2] – says that the inverse of a rank- k correction of some matrix can be computed by doing a rank- k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman ...
Sherman–Morrison formula. In linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of a " rank -1 update" to a matrix whose inverse has previously been computed. [ 1 ][ 2 ][ 3 ] That is, given an invertible matrix and the outer product of vectors and the formula cheaply ...
Block matrix. Matrix defined using smaller matrices called blocks. In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1][2] Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of ...
hide. In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called ...
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃəˈlɛski / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the 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 ...