IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2738-d878671.html
   My bibliography  Save this article

Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation

Author

Listed:
  • Ashim Kumar

    (Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala 144603, India)

  • Dijana Mosić

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

  • Predrag S. Stanimirović

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

  • Gurjinder Singh

    (Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala 144603, India)

  • Lev A. Kazakovtsev

    (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia)

Abstract

This paper investigates new solution sets for the Yang–Baxter-like (YB-like) matrix equation involving constant entries or rational functional entries over complex numbers. Towards this aim, first, we introduce and characterize an essential class of generalized outer inverses (termed as { 2 , 5 } -inverses) of a matrix, which commute with it. This class of { 2 , 5 } -inverses is defined based on resolving appropriate matrix equations and inner inverses. In general, solutions to such matrix equations represent optimization problems and require the minimization of corresponding matrix norms. We decided to analytically extend the obtained results to the derivation of explicit formulae for solving the YB-like matrix equation. Furthermore, algorithms for computing the solutions are developed corresponding to the suggested methods in some computer algebra systems. The main features of the proposed approach are highlighted and illustrated by numerical experiments.

Suggested Citation

  • Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2738-:d:878671
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2738/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2738/
    Download Restriction: no
    ---><---

    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. Duanmei Zhou & Jiawen Ding, 2020. "All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two," Complexity, Hindawi, vol. 2020, pages 1-7, June.
    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. Kumar, Ashim & Cardoso, João R., 2018. "Iterative methods for finding commuting solutions of the Yang–Baxter-like matrix equation," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 246-253.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Stanimirović, Predrag S. & Mosić, Dijana & Wei, Yimin, 2022. "Generalizations of composite inverses with certain image and/or kernel," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    3. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    4. 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).
    5. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
    7. 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).
    8. Shanshan Hu & Yongxin Yuan, 2023. "Common Solutions to the Matrix Equations $$AX=B$$ A X = B and $$XC=D$$ X C = D on a Subspace," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 372-386, July.
    9. Haifa Bin Jebreen, 2019. "Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme," Mathematics, MDPI, vol. 7(8), pages 1-11, August.
    10. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2738-:d:878671. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.