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

Milan Mišić, Marina Tošić, Zoran J. Popović

In this paper we give a representation of the Moore--Penrose inverse and the group inverse of a linear combination of Moore--Penrose Hermitian matrices, i.e., square matrices satisfying $A^{\dag}=A$. Also, we consider the invertibility of some linear combination of commuting Moore--Penrose Hermitian matrices.