Properties of core-EP matrices and binary relationships

Ehsan Kheirandish; Abbas Salemi; Néstor Thome

doi:10.1007/s40314-024-02836-x

Properties of core-EP matrices and binary relationships

Numerical Analysis 2024-07-09 v2 Numerical Analysis

Authors: Ehsan Kheirandish , Abbas Salemi , Néstor Thome

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Abstract

In this paper, various properties of core-EP matrices are investigated. We introduce the MPDMP matrix associated with $A$ and by means of it, some properties and equivalent conditions of core-EP matrices can be obtained. Also, properties of MPD, DMP, and CMP inverses are studied and we prove that in the class of core-EP matrices, DMP, MPD, and Drazin inverses are the same. Moreover, DMP and MPD binary relation orders are introduced and the relationship between these orders and other binary relation orders are considered.

Keywords

generalized inverses hadamard matrices

Cite

@article{arxiv.2407.02602,
  title  = {Properties of core-EP matrices and binary relationships},
  author = {Ehsan Kheirandish and Abbas Salemi and Néstor Thome},
  journal= {arXiv preprint arXiv:2407.02602},
  year   = {2024}
}