Least Squares Properties of Generalized Inverses

Abstract

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses. As a significant application of the Moore-Penrose inverse, the best approximation solution to linear matrix equations (i.e. both least squares and the minimal norm) is considered. Also, characterizations of least squares solution and solution of minimum norm are given. Basic properties of the Drazin-inverse solution and the outer-inverse solution are present. Motivated by recent research, important least square properties of composite outer inverses are collected.