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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
$A_1X=C_1, \qquad XB_3=C_3$
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:
 15A24 Matrix equations and identities 15B33 Matrices over special rings (quaternions, finite fields, etc.)
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##### References:
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