Matrix Equation’s Reflexive and Anti-Reflexive Solutions over Quaternions
Xin Liu,
Kaiqi Wen,
Yang Zhang
Affiliations
Xin Liu
Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Macau 999078, China
Kaiqi Wen
Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Macau 999078, China
Yang Zhang
Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
We consider when the quaternion matrix equation AXB+CXD=E has a reflexive (or anti-reflexive) solution with respect to a given generalized reflection matrix. We adopt a real representation method to derive the solutions when it is solvable. Moreover, we obtain the explicit expressions of the least-squares reflexive (or anti-reflexive) solutions.
