Further characterizations of the CMP inverse of matrices.

In this paper, we give simple characterizations of the CMP inverse to be an EP matrix and simplify Theorem 2.10 in [New characterizations of the CMP inverse of matrices. Linear Multilinear Algebra. 2020;68(4):790–804]. Also, we characterize the CMP inverse of a matrix based on its range space and null space. Several different representations of the CMP inverse are given. In addition, some new characterizations of k-commutative equalities for some outer generalized inverse are investigated in terms of the CMP inverse. [ABSTRACT FROM AUTHOR]