An Orthogonalization Method of Computing the Generalized Inverse of a Matrix

摘要

A method of computing the generalized inverse of a matrix is derived from the behavior of a linear transformation and its generalized inverse relative to the range and null space of the operator. The method utilizes the gram-schmidt procedure to obtain an orthogonal basis for the column space of the matrix, and then the biorthogonalization technique of Hestenes to obtain the inverse of a matrix that has the same rank as the original. A matrix multiplication then yields the required generalized inverse. (Author)