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Hua’s Identity for the \(\{1, 2\}\)-Inverse

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Abstract

In this paper, we generalized Hua’s identity to the \(\{1, 2\}\)-inverse case. In addition, theconditions that make Hua’s identities true for the Moore–Penrose inverse, group inverse, core inverse and dual core inverse are given, respectively.

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Acknowledgements

The authors are highly grateful to the anonymous referees who has provided the helpful comments and suggestions. Authors would like to thank Prof. Pu Zhang for the question he raised: whether the Loo-Keng Hua identity is true for generalized inverses. This research is supported by the National Natural Science Foundation of China (no. 11771076); the Fundamental Research Funds For the Central Universities (no. KYCX17_0037); Postgraduate Research & Practice Innovation Program of Jiangsu Province (no. KYCX17_0037). The third author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 174007.

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Authors and Affiliations

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

    Tingting Li & Jianlong Chen

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

    Dijana Mosić

Authors
  1. Tingting Li
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  2. Jianlong Chen
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  3. Dijana Mosić
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Correspondence to Jianlong Chen.

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Communicated by Abbas Salemi.

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Li, T., Chen, J. & Mosić, D. Hua’s Identity for the \(\{1, 2\}\)-Inverse. Bull. Iran. Math. Soc. 46, 323–330 (2020). https://doi.org/10.1007/s41980-019-00259-7

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  • DOI: https://doi.org/10.1007/s41980-019-00259-7

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