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.


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


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