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An extension of the MPD and MP weak group inverses

Author

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  • Mosić, Dijana
  • Zhang, Daochang
  • Stanimirović, Predrag S.

Abstract

Combining the Moore-Penrose (MP) inverse with m-weak group inverse (m-WGI) in an appropriate way, we solve certain systems of equations and establish a novel class of generalized inverses, which is called the Moore-Penrose m-WGI (MP-m-WGI). Since the weak group inverse (WGI) and Drazin inverse are particular instances of the m-WGI family, it clearly follows that MP weak group (MPWG) inverse and MPD inverse are subclasses of the MP-m-WGI. We present a number of effective representations and characterizations for the MP-m-WGI. As corollaries, we propose new generalized inverses and validate some known properties and representations of the MPD inverse. The MP-2-WGI is considered as one important kind of the MP-m-WGI. Continuity of the MP-m-WGI is studied too. Solvability of a few linear equations is proved and general solutions are expressed as expressions which include the MP-m-WGI.

Suggested Citation

  • Mosić, Dijana & Zhang, Daochang & Stanimirović, Predrag S., 2024. "An extension of the MPD and MP weak group inverses," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    • Handle: RePEc:eee:apmaco:v:465:y:2024:i:c:s0096300323005982
    DOI: 10.1016/j.amc.2023.128429
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    References listed on IDEAS

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    1. Na Liu & Hongxing Wang & Efthymios G. Tsionas, 2021. "The Characterizations of WG Matrix and Its Generalized Cayley–Hamilton Theorem," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, December.
    2. Ferreyra, D.E. & Levis, F.E. & Thome, N., 2018. "Maximal classes of matrices determining generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 42-52.
    3. Zhou, Mengmeng & Chen, Jianlong, 2018. "Integral representations of two generalized core inverses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 187-193.
    4. Ivan I. Kyrchei, 2019. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications," Journal of Mathematics, Hindawi, vol. 2019, pages 1-13, October.
    5. Mosić, Dijana & Stanimirović, Predrag S., 2021. "Representations for the weak group inverse," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    6. Ma, Haifeng & Gao, Xiaoshuang & Stanimirović, Predrag S., 2020. "Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    8. Ma, Haifeng & Stanimirović, Predrag S., 2019. "Characterizations, approximation and perturbations of the core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 404-417.
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