IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p450-d1579399.html
   My bibliography  Save this article

A Survey on Solving the Matrix Equation AXB = C with Applications

Author

Listed:
  • Qing-Wen Wang

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
    Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China)

  • Lv-Ming Xie

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China)

  • Zi-Han Gao

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China)

Abstract

This survey provides a comprehensive overview of the solutions to the matrix equation A X B = C over real numbers, complex numbers, quaternions, dual quaternions, dual split quaternions, and dual generalized commutative quaternions, including various special solutions. Additionally, we summarize the numerical algorithms for these special solutions. This matrix equation plays an important role in solving linear systems and control theory. We specifically explore the application of this matrix equation in color image processing, highlighting its unique value in this field. Taking the dual quaternion matrix equation A X B = C as an example, we design a scheme for simultaneously encrypting and decrypting two color images. The experimental results demonstrate that this scheme is highly feasible.

Suggested Citation

  • Qing-Wen Wang & Lv-Ming Xie & Zi-Han Gao, 2025. "A Survey on Solving the Matrix Equation AXB = C with Applications," Mathematics, MDPI, vol. 13(3), pages 1-50, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:450-:d:1579399
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/450/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/450/
    Download Restriction: no
    ---><---

    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:13:y:2025:i:3:p:450-:d:1579399. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.