A new generalized inverse for rectangular matrices

Abstract

The goal of this paper is to introduce a new generalized inverse, called the MMP-inverse along a matrix. Let [Formula: see text] be the set of [Formula: see text] complex matrices. Given any [Formula: see text] and [Formula: see text], the matrix [Formula: see text] is called MMP-invertible along [Formula: see text] if there exists a matrix [Formula: see text] such that [Formula: see text] and [Formula: see text]. Such an [Formula: see text] is called an MMP-inverse of [Formula: see text] along [Formula: see text]. Some characterizations of the MMP-inverse along a matrix are given by its range and null space. Also, the connection between the MMP-inverse along a matrix and other generalized inverses is investigated. Finally, the formula for the MMP-inverse of matrices is expressed.