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

Ruopeng Liao, Xin Liu (), Sujuan Long and Yang Zhang
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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

Mathematics, 2024, vol. 12, issue 2, 1-12

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.

Keywords: quaternion matrix equation; ( R , S )-(skew) symmetric; real representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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