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Explicit formulae for the Drazin inverse of the sum of two matrices

  • Daochang Zhang , Yue Zhao EMAIL logo and Dijana Mosić
Published/Copyright: February 25, 2025
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Abstract

In this article, we construct a new explicit formula for the Drazin inverse of a sum of two matrices P, Q ∈ ℂn×n under conditions weaker than those used in some recent papers, and modify an invalid formula in [Dopazo et al.: Block representations for the Drazin inverse of anti-triangular matrices, Filomat 30 (2016), 3897–3906]. Furthermore, we apply our results to obtain some new representations for the Drazin inverse of a 2 × 2 block matrix. Some numerical examples are given to illustrate our results.

MSC 2010: 15A09; 39B42; 65F20

The first author is supported by the National Natural Science Foundation of China (NSFC) (No. 11901079; No. 61672149), and China Postdoctoral Science Foundation (No. 2021M700751), and the Scientific and Technological Research Program Foundation of Jilin Province (No. JJKH20190690KJ; No. 20200401085GX; No. JJKH20220091KJ). The third author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (No. 451-03-68/2022-14/200124) and the bilateral project between Serbia and Slovenia (Generalized inverses, operator equations and applications, No. 337-00-21/2020-09/32).


  1. (Communicated by Gregor Dolinar)

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Received: 2024-04-22
Accepted: 2024-08-26
Published Online: 2025-02-25
Published in Print: 2025-02-25

© 2025 Mathematical Institute Slovak Academy of Sciences

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