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A System of Four Generalized Sylvester Matrix Equations over the Quaternion Algebra

Author

Listed:
  • Zhuo-Heng He

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

  • Jie Tian

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

  • Shao-Wen Yu

    (School of Mathematics, East China University of Science and Technology, Shanghai 200237, China)

Abstract

In this paper, we make use of the simultaneous decomposition of eight quaternion matrices to study the solvability conditions and general solutions to a system of two-sided coupled Sylvester-type quaternion matrix equations A i X i C i + B i X i + 1 D i = Ω i , i = 1 , 2 , 3 , 4 . We design an algorithm to compute the general solution to the system and give a numerical example. Additionally, we consider the application of the system in the encryption and decryption of color images.

Suggested Citation

  • Zhuo-Heng He & Jie Tian & Shao-Wen Yu, 2024. "A System of Four Generalized Sylvester Matrix Equations over the Quaternion Algebra," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2341-:d:1443810
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    References listed on IDEAS

    as
    1. Bilal Ahmad Rather & Hilal A. Ganie & Kinkar Chandra Das & Yilun Shang, 2024. "The General Extended Adjacency Eigenvalues of Chain Graphs," Mathematics, MDPI, vol. 12(2), pages 1-16, January.
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