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A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

Author

Listed:
  • Long-Sheng Liu

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Qing-Wen Wang

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

  • Mahmoud Saad Mehany

    (Department of Mathematics, Shanghai University, Shanghai 200444, China
    Department of Mathematics, Ain Shams University, Cairo 11566, Egypt)

Abstract

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η -Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.

Suggested Citation

  • Long-Sheng Liu & Qing-Wen Wang & Mahmoud Saad Mehany, 2022. "A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application," Mathematics, MDPI, vol. 10(10), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1758-:d:820675
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    References listed on IDEAS

    as
    1. Tao Li & Qing-Wen Wang & Xin-Fang Zhang, 2022. "A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    2. Liu, Xin, 2018. "The η-anti-Hermitian solution to some classic matrix equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 264-270.
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