Abstract
In this paper 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 A X = C and the following system { A 1 X = C 1 X B 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.
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