A system of matrix equations over regular rings

作者：Lin Chun Yan^*; Wang Qing Wen; Qin Feng

来源：Indian Journal of Pure and Applied Mathematics, 2007, 38(6): 517-532.

• system of matrix equations
• regular ring
• inner inverse of a matrix
• reflexive inverse of a matrix
• centrosymmetric solution

In this paper, we establish necessary and sufficient conditions for the existence of the general solution to the system of five linear matrix equations X1B1 = C-1, X1B2 = C-2,X2B3 = C-3, X2B4 = C-4, A(5)X(1)B(5) + A(6)X(2)B(6) = C-5 over an arbitrary regular ring with identity R. An expression of the general solution to the system is also derived when the solvable conditions are satisfied. As an application, necessary and sufficient conditions for the existence and a representation of the centrosymmetric solution to the system of matrix equations XBa = C-

• 出版日期2007-12
• 单位上海大学; 山东财经大学