## 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.)
Full Text:

### References:

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