Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations

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 A1X = C-1, A(1)x = C-1, XB3 = C-3, A(2)X = C-2, to have bisymmetric solutions, and the system A(1)X = C-1, A(3)XB(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. (c) 2005 Elsevier Ltd. All rights reserved.