Revisiting the core EP inverse and its extension to rectangular matrices.

In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, <italic>Linear and Multilinear Algebra</italic><bold>62</bold>(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. [ABSTRACT FROM AUTHOR]