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Drazin-Star and Star-Drazin Matrices

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Abstract

The aim of this paper is to introduce two new classes of square matrices, which are called the Drazin-star and star-Drazin matrices, in order to solve some type of matrix equations. Several characterizations of these new matrices are given. Some relations between various well-known generalized inverses and the Drazin-star and star-Drazin matrices are investigated. We present the integral representations, the limit representations and representations based on the full-rank decomposition for the Drazin-star and star-Drazin matrices. Applying these results for a square matrix of index one, we define and study the group-star and star-group matrices.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000, Niš, Serbia

    Dijana Mosić

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  1. Dijana Mosić
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The author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant Number 174007.

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Mosić, D. Drazin-Star and Star-Drazin Matrices. Results Math 75, 61 (2020). https://doi.org/10.1007/s00025-020-01191-7

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  • DOI: https://doi.org/10.1007/s00025-020-01191-7

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