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Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations. (English) Zbl 1138.15003
Summary: In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra $\Bbb H$. Necessary and sufficient conditions are obtained for the matrix equation $AX = C$ and the following systems \aligned A_1X&=C_1,\\ XB_3&=C_3,\endaligned \quad \quad \aligned A_1X&=C_1,\\ A_2X&=C_2,\endaligned to have bisymmetric solutions, and the system \align A_1X & =C_1,\\ A_3 XB_3 & =C_3,\endalign 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 $\Bbb H$ are also mentioned.

##### MSC:
 15A24 Matrix equations and identities 15B33 Matrices over special rings (quaternions, finite fields, etc.)
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##### References:
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