(<i>R</i>, <i>S</i>)-(Skew) Symmetric Solutions to Matrix Equation <i>AXB</i> = <i>C</i> over Quaternions
Ruopeng Liao,
Xin Liu,
Sujuan Long,
Yang Zhang
Affiliations
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
(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 AXB=C. We use a real representation Aτ to obtain the necessary and sufficient conditions for AXB=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.
