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

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 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.

Keywords

• quaternion matrix equation
• (<i>R</i>, <i>S</i>)-(skew) symmetric
• real representation