A new expression for the Moore-Penrose inverse of a class of matrices

Abstract

An expression for the Moore-Penrose inverse of a matrix of the form M = XNY , where X and Y are nonsingular, has been recently established by Castro-González et al. [1, Theorem 2.2]. The expression plays an essential role in developing explicit expressions for the Moore-Penrose inverse of a two-by-two block matrix. In this paper, we present a new expression for the Moore-Penrose inverse of this class of matrices, which improves the result in [1].