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Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. [ 2] Over a field, a square matrix that is not invertible is called singular or degenerate. A square matrix with entries in a field is singular if and only if its determinant is zero.
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 ...
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 computes ...
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 ...
Inverse-Wishart. In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution.
In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method . It appears to have originally been developed to ...
Generalized inverse. In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. 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 ...
Inverse distance weighting ( IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial ...
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