Core-EP Decomposition and its Applications

TL;DR

This paper introduces the core-EP decomposition, explores its properties, and uses it to characterize the core-EP inverse, as well as defining and analyzing new order relations in matrix theory.

Contribution

It presents the novel concept of core-EP decomposition and applies it to characterize the core-EP inverse and define new matrix orders.

Findings

Characterization of the core-EP inverse using the decomposition

Introduction of the core-EP order and core-minus partial order

Properties and characterizations of the new orders

Abstract

In this paper, we introduce the notion of the core-EP decomposition and some of its properties. By using the decomposition, we derive several characterizations of the core-EP inverse, introduce a pre-order(i.e. the core-EP order) and a partial order(i.e. the core-minus partial order), and characterize the properties of both orders.