Expressions and characterizations for the moore-penrose inverse of operators and matrices

Abstract

Under certain conditions, we prove that the Moore—Penrose inverse of a sum of operators is the sum of the Moore—Penrose inverses. From this, we derive expressions and characterizations for the Moore—Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore—Penrose inverse of circulant matrices and of distance matrices of certain graphs.