Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 533-546.doi: 10.1007/s42967-024-00452-4

• ORIGINAL PAPERS • Previous Articles     Next Articles

The Leslie Matrix Solution of the Reduced Biquaternion Matrix Equation AXB+CXD=E

Jiaxin Lan1, Jingpin Huang2, Dan Huang3   

  1. 1. School of Humanities and Education, Guangxi Financial Vocational College, Nanning, 530007, Guangxi, China;
    2. College of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, Guangxi, China;
    3. School of Computer Science and Engineering, Yulin Normal University, Yulin, 537000, Guangxi, China
  • Received:2024-03-09 Revised:2024-08-01 Online:2026-04-07 Published:2026-04-07
  • Contact: Jiaxin Lan,E-mail:xinjlan@qq.com E-mail:xinjlan@qq.com
  • Supported by:
    This work was supported by the 2024 School-Level Project of Guangxi Financial Vocational College (No. 607001), the National Natural Science Foundation of China (No. 12361078), the Sichuan Science and Technology Program (No. 2024NSFSC0721), the Postdoctoral Fellowship Program of CPSF (No. GZB20230092), and the China Postdoctoral Science Foundation (No. 2023M740383).

Abstract: This paper investigates two different Leslie matrix solutions for the reduced biquaternion matrix equation \begin{document}$ AXB+CXD=E $\end{document}. Through the permutation matrices, the complex decomposition of reduced biquaternion matrices, and the Kronecker product, by leveraging the specific attributes of Leslie matrices, we transform the constrained reduced biquaternion matrix equation into an unconstrained form. Consequently, we derive the necessary and sufficient conditions for the existence of solutions in the form of Leslie matrices to the reduced biquaternion matrix equation \begin{document}$ AXB+CXD=E $\end{document} and provide a general expression for such solutions. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

Key words: Reduced biquaternion, Leslie matrix, Kronecker product, Complex decomposition, Optimal approximation

CLC Number: