Least Squares Properties of Generalized Inverses (Communications in Mathematical Research, 2022)
The aim of this paper is to systematize solutions of some systems oflinear equations in terms of generalized inverses. As a significant applicationof the Moore-Penrose inverse, the best approximation solution to linear matrixequations (i.e. both least squares and the minimal norm) is considered. Also,characterizations of least squares solution and solution of minimum norm aregiven. 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.
Keywords: Outer inverse; Moore-Penrose inverse; DMP inverse; core-EP inverse.