Abstract
In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra ℍ . Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systems A 1 X = C 1 , A 1 X = C 1 , X B 3 = C 3 , A 2 X = C 2 , to have bisymmetric solutions, and the system A 1 X = C 1 , A 3 X B 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 ℍ are also mentioned.
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