Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations

In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra @?. Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systemsA"1X=C"1,A"1X=C"1,XB"3=C"3,A"2X=C"2, to have bisymmetric solutions, and the systemA"1X=C"1,A"3XB"3=C"3, to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over @? are also mentioned.

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