Representations for the weak group inverse

Abstract

The aim of this paper is to provide new representations and characterizations of the weak group inverse. We give a relation between the weak group inverse and a corresponding nonsingular border matrix. Continuity of weak group inverse is studied. Several limit representations, integral representations and perturbation formulae for the weak group inverse are proposed. Various expressions for the weak group and core–EP inverses of upper block triangular matrix are established and their sign patterns are considered. The splitting method for finding weak group inverse is proved as well as the successive matrix squaring algorithm for computing weak group inverse. Also, the weak group inverse can be used in solving appropriate systems of linear equations.