Three limit representations of the core-EP inverse

TL;DR

This paper introduces three new limit representations for the core-EP inverse and its dual, utilizing matrix decompositions and explicit formulas, enhancing understanding and computation of these inverses.

Contribution

The paper provides three novel limit representations of the core-EP inverse, including approaches based on full-rank decomposition and explicit expressions, along with dual inverse representations.

Findings

Three limit representations of the core-EP inverse are established.

Limit representations of the dual core-EP inverse are derived.

New methods improve understanding and computation of core-EP inverses.

Abstract

In this paper, we present three limit representations of the core-EP inverse. The first approach is based on the full-rank decomposition of a given matrix. The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived