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( R , S )-(Skew) Symmetric Solutions to Matrix Equation AXB = C over Quaternions

Author

Listed:
  • Ruopeng Liao

    (School of Computer Science and Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau 999078, China)

  • Xin Liu

    (Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau 999078, China)

  • Sujuan Long

    (School of Mathematics and Data Science, Minjiang University, Fujian 350108, China)

  • Yang Zhang

    (Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada)

Abstract

( R , S )-(skew) symmetric matrices have numerous applications in civil engineering, information theory, numerical analysis, etc. In this paper, we deal with the ( R , S )-(skew) symmetric solutions to the quaternion matrix equation A X B = C . We use a real representation A τ to obtain the necessary and sufficient conditions for A X B = C to have ( R , S )-(skew) symmetric solutions and derive the solutions when it is consistent. We also derive the least-squares ( R , S )-(skew) symmetric solution to the above matrix equation.

Suggested Citation

  • Ruopeng Liao & Xin Liu & Sujuan Long & Yang Zhang, 2024. "( R , S )-(Skew) Symmetric Solutions to Matrix Equation AXB = C over Quaternions," Mathematics, MDPI, vol. 12(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:323-:d:1322007
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