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.
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