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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 \(\mathbb H\). Necessary and sufficient conditions are obtained for the matrix equation \(AX = C\) and the following systems
\[ \begin{aligned} A_1X&=C_1,\\ XB_3&=C_3,\end{aligned} \quad \quad \begin{aligned} A_1X&=C_1,\\ A_2X&=C_2,\end{aligned} \]
to have bisymmetric solutions, and the system
\[ \begin{aligned} A_1X & =C_1,\\ A_3 XB_3 & =C_3,\end{aligned} \]
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 \(\mathbb H\) are also mentioned.

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