Properties of core-EP matrices and binary relationships
Ehsan Kheirandish, Abbas Salemi, N\'estor Thome
TL;DR
This paper explores properties of core-EP matrices, introduces the MPDMP matrix, and studies inverse relations, revealing that DMP, MPD, and Drazin inverses coincide within core-EP matrices.
Contribution
It introduces the MPDMP matrix and establishes equivalences and relations among various inverses and binary orderings for core-EP matrices.
Findings
DMP, MPD, and Drazin inverses are identical in core-EP matrices.
Properties and equivalent conditions of core-EP matrices are characterized.
Binary relation orders DMP and MPD are defined and related to other orders.
Abstract
In this paper, various properties of core-EP matrices are investigated. We introduce the MPDMP matrix associated with 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.
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