 This article describes generalized inverses of a matrix formula_1.Formally, given a matrix formula_2 and a matrix formula_3, formula_4 is a generalized inverse of formula_1 if it satisfies the condition formula_6

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 than invertible matrices.A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse.