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Representations for the Drazin Inverse of the Sum of Two Matrices and its Applications

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Abstract

Some additive results for the Drazin inverses are investigated under conditions weaker than those used in some recent papers on this subject. In particular, a formula is given for the Drazin inverse of a sum of two matrices \(P, Q\in {\mathbf {C}}^{n\times n}\) with \(PQ^{i}P=0\) for positive integer \(i=1,2,\ldots ,n\). As an application we give some new representations for the Drazin inverse of a \(2 \times 2\) block matrix.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Li Guo & Jianlong Chen

  2. School of Mathematics and Statistics, Beihua University, Jilin, 132013, China

    Li Guo

  3. School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

    Honglin Zou

Authors
  1. Li Guo
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  2. Jianlong Chen
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  3. Honglin Zou
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Corresponding author

Correspondence to Li Guo.

Additional information

Communicated by Abbas Salemi.

This work was supported by the National Natural Science Foundation of China (No.11771076), Natural Science Foundation of Jilin Province of China (No.20160101264JC), Foundation of Jilin Educational Committee (No.JJKH20180333KJ), Youth Fostering Foundation of Beihua University (No.2017QNJJL12) and China Postdoctoral Science Foundation (No.2018M632385).

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Guo, L., Chen, J. & Zou, H. Representations for the Drazin Inverse of the Sum of Two Matrices and its Applications. Bull. Iran. Math. Soc. 45, 683–699 (2019). https://doi.org/10.1007/s41980-018-0159-x

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  • DOI: https://doi.org/10.1007/s41980-018-0159-x

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