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The Drazin inverse of anti-triangular block matrices

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Abstract

The aim of this paper is to establish formulae for the Drazin inverse of anti-triangular block matrices under new assumptions in literature. Precisely, we consider the Drazin inverse of three kinds of anti-triangular block matrices. Applying these results, we present new expressions for the Drazin inverse of an arbitrary block matrix. In this way, we generalize a list of earlier results and illustrate it with three examples.

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Acknowledgements

The authors are thankful for the editor and the referees for their very useful comments and suggestions.

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Authors and Affiliations

  1. College of Sciences, Northeast Electric Power University, Jilin, People’s Republic of China

    Daochang Zhang & Yu Jin

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

    Dijana Mosić

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  1. Daochang Zhang
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  2. Yu Jin
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  3. Dijana Mosić
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Correspondence to Daochang Zhang.

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The first author is supported by the National Natural Science Foundation of China (NSFC) (Nos. 11901079, 61672149), and the Scientific and Technological Research Program Foundation of Jilin Province, China (Nos. 20190201095JC, 20200401085GX). The third author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (No. 174007/451-03-9/2021-14/200124) and the bilateral project between Serbia and Slovenia (Generalized inverses, operator equations and applications, No. 337-00-21/2020-09/32).

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Zhang, D., Jin, Y. & Mosić, D. The Drazin inverse of anti-triangular block matrices. J. Appl. Math. Comput. 68, 2699–2716 (2022). https://doi.org/10.1007/s12190-021-01638-2

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  • DOI: https://doi.org/10.1007/s12190-021-01638-2

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