The matrix equation a256e897" title="Click to view the MathML source">AX−XB=C has a solution if and only if the matrices and are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation 40a43ad0b" title="Click to view the MathML source">X−AXB=C over a field has a solution if and only if the matrices and are simultaneously equivalent to and . We extend these criteria to the matrix equations 40a65991019adbba250d6d84ea3be"> and over the skew field of quaternions with a fixed involutive automorphism .
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