作者：QingWenWANG冯诺伊曼正则环矩阵方程中心对称矩阵共轭矩阵
摘要：We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results.
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