The E -relative m -weak group inverse

Abstract

In this paper the notion of the m-weak group inverse of a complexsquare matrix relative to an invertible Hermitian weight E is introduced.We show several equivalent algebraic characterizations of this new type ofgeneralized inverse. Additionally, different properties, representations, andcharacterizations involving the column space, null space, rank equalities, andprojectors are presented. Finally, we solve a linear equation using this newgeneralized inverse.