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Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations. (English) Zbl 1143.15012

Summary: We consider symmetric and skew-antisymmetric solutions to certain matrix equations over the real quaternion algebra H. First, a criterion for a quaternion matrix to be symmetric and skew-antisymmetric is given. Then, necessary and sufficient conditions are obtained for the matrix equation AX=C and the following system

A 1 X=C 1 ,XB 3 =C 3

to have symmetric and skew-antisymmetric solutions. The expressions of such solutions of the matrix equation and the system mentioned above are also given.

MSC:
15A24Matrix equations and identities
15A33Matrices over special rings
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