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

TL;DR

This paper introduces an improved explicit formula for the Moore-Penrose inverse of matrices of the form M = XNY, enhancing previous results and aiding in the analysis of block matrices.

Contribution

It presents a new, more effective expression for the Moore-Penrose inverse of matrices of the form M = XNY, improving upon existing formulas.

Findings

Provides a more efficient formula for the Moore-Penrose inverse

Enhances the analysis of two-by-two block matrices

Simplifies computations involving these 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-Gonz\'alez 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].