Some results on core EP Drazin matrices and partial isometries

TL;DR

This paper introduces the new class of core EP Drazin matrices, explores their properties, and investigates conditions under which partial isometries belong to this class, supported by numerical examples.

Contribution

It defines the novel class of core EP Drazin matrices and analyzes their properties and relations to partial isometries, expanding the understanding of generalized inverses.

Findings

Core EP Drazin matrices include EP and normal matrices.

Conditions for partial isometries to be CEPD are established.

Numerical examples illustrate the main theoretical results.

Abstract

In this paper, by using the core EP inverse and the Drazin inverse which are two well known generalized inverses, a new class of matrices entitled core EP Drazin matrices (shortly, CEPD matrices) is introduced. This class contains the set of all EP matrices and also the set of normal matrices. Some algebraic properties of these matrices are also investigated. Moreover, some results about the Drazin inverse and the core EP inverse of partial isometries are derived, and using them, some conditions for which partial isometries are CEPD, are obtained. To illustrate the main results, some numerical examples are given.