New characterizations of weak group matrices

Abstract

In this paper, we prove that a complex square matrix is weak group matrix if the m-th power of this matrix commutes with its weak group inverse, where m is an arbitrary positive integer. Firstly,
some new characterizations of weak group matrices are investigated by means of core-EP decomposition. Secondly, we study new equivalent conditions of the weak group matrix by using commutator and rank equalities. Finally, the relationships between{m,k}-core EP matrices, k-EP matrices and weak group matrices are given.