Generalized Inverses of a Linear Combination of Moore-Penrose Hermitian Matrices

Abstract

In this paper we give a representation of the Moore-Penrose inverse, i.e., the group inverse of a linear combination of Moore-Penrose hermitian matrices, i.e., square matrices satisfying A^†=A. Also, we consider the invertibility of some linear combination of commuting Moore-Penrose hermitian matrices.