Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices

Mortezaei, Mahdiyeh; Aghamollaei, Gholamreza

doi:10.22103/jmmr.2023.21769.1462

Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices

Document Type : Research Paper

Authors

Mahdiyeh Mortezaei ¹

Gholamreza Aghamollaei ¹^{, 2}

¹ Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

² Mahani Mathematical Research Institute, Shahid Bahonar University of Kerman, Kerman, Iran

10.22103/jmmr.2023.21769.1462

Abstract

In this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse and
the Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore-Penrose inverse, the Drazin inverse and the numerical range of some reciprocal matrices are obtained. In particular, the relations between reciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP matrices are studied. To illustrate the results, some numerical examples are also given.

Keywords

Moore-Penrose inverse

Drazin inverse

reciprocal matrices

numerical range

conjugate EP matrices

Subjects

Analysis

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