Revisiting the core EP inverse and its extension to rectangular matrices

Abstract

In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra 62(3) (2014), 792-802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses.

Keywords: Generalized inverses, Moore-Penrose inverse, core inverse, generalized core inverse, core EP inverse, DMP generalized inverse