New characterizations of the generalized Moore-Penrose inverse of matrices

Abstract

Some new characterizations of the generalized Moore-Penrose inverse are proposed using range, null space, several matrix equations and projectors. Several representations of the generalized Moore-Penrose inverse are given. The relationships between the generalized Moore-Penrose inverse and other generalized inverses are discussed using core-EP decomposition. The generalized Moore-Penrose matrices are introduced and characterized. One relation between the generalized Moore-Penrose inverse and corresponding nonsingular border matrix is presented. In addition, applications of the generalized Moore-Penrose inverse in solving restricted matrix equations are studied.

Keywords

• generalized moore-penrose inverse
• range space
• null space
• core-ep decomposition