IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v513y2026ics0096300325005041.html

On the solution of the quaternion matrix equation A⋉ΓX⋉ΓB=C

Author

Listed:
  • Wang, Aifa
  • Sun, Xiaotao
  • Wang, Lili

Abstract

In this paper, we investigate the solvability of the matrix equation A⋉ΓX⋉ΓB=C in both the real and quaternion fields, utilizing the generalized semi-tensor product notation⋉Γ. By converting the original equation into the standard form Ax=b via column stacking, we employ the Moore-Penrose inverse (M-P inverse) to derive the necessary and sufficient conditions for a solution’s existence. Furthermore, we present an efficient MATLAB implementation for solving the matrix equation and provide numerical experiments to validate the algorithm’s correctness and computational efficiency.

Suggested Citation

  • Wang, Aifa & Sun, Xiaotao & Wang, Lili, 2026. "On the solution of the quaternion matrix equation A⋉ΓX⋉ΓB=C," Applied Mathematics and Computation, Elsevier, vol. 513(C).
    • Handle: RePEc:eee:apmaco:v:513:y:2026:i:c:s0096300325005041
    DOI: 10.1016/j.amc.2025.129779
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325005041
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129779?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Fengxia & Wei, Musheng & Li, Ying & Zhao, Jianli, 2015. "Special least squares solutions of the quaternion matrix equation AX=B with applications," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 425-433.
    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.

      More about this item

      Keywords

      ;
      ;
      ;
      ;

      Statistics

      Access and download statistics

      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:eee:apmaco:v:513:y:2026:i:c:s0096300325005041. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

      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.