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Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space

Author

Listed:
  • Dijana Mosić

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia)

  • Predrag S. Stanimirović

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
    Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia)

  • Spyridon D. Mourtas

    (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia
    Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

Abstract

The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a particular case we extend some well-known results and give several new results for the weak Drazin inverse. The main characterizations of the Drazin inverse, group inverse and Moore–Penrose inverse are obtained as consequences.

Suggested Citation

  • Dijana Mosić & Predrag S. Stanimirović & Spyridon D. Mourtas, 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1732-:d:1116260
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    References listed on IDEAS

    as
    1. Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    2. Kansal, Munish & Kumar, Sanjeev & Kaur, Manpreet, 2022. "An efficient matrix iteration family for finding the generalized outer inverse," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Predrag S. Stanimirović & Miroslav Ćirić & Igor Stojanović & Dimitrios Gerontitis, 2017. "Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses," Complexity, Hindawi, vol. 2017, pages 1-27, June.
    4. Cordero, Alicia & Soto-Quiros, Pablo & Torregrosa, Juan R., 2021. "A general class of arbitrary order iterative methods for computing generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Stanimirović, Predrag S. & Mourtas, Spyridon D. & Mosić, Dijana & Katsikis, Vasilios N. & Cao, Xinwei & Li, Shuai, 2024. "Zeroing neural network approaches for computing time-varying minimal rank outer inverse," Applied Mathematics and Computation, Elsevier, vol. 465(C).

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