摘要
We consider the system of four linear matrix equations A_1 X = C_1,XB_2 =C_2,A_3,XB_3, = C3 and A_4XB_4 = C_4 over R, an arbitrary von Neumann regular ring with identity. Anecessary and sufficient condition for the existence and the expression of the general solution tothe system are derived. As applications, necessary and sufficient conditions are given for thesystem of matrix equations A_1X = C_1 and A_3X = C_3 to have a bisymmetric solution, the system ofmatrix equations A_1X = C_1 and A_3XB_3 = C_3 to have a perselfconjugate solution over R with aninvolution and char R≠2, respectively. The representations of such solutions are also presented.Moreover, some auxiliary results on other systems over R are obtained. The previous known results onsome systems of matrix equations are special cases of the new results.
We consider the system of four linear matrix equations A_1 X = C_1,XB_2 =C_2,A_3,XB_3, = C3 and A_4XB_4 = C_4 over R, an arbitrary von Neumann regular ring with identity. Anecessary and sufficient condition for the existence and the expression of the general solution tothe system are derived. As applications, necessary and sufficient conditions are given for thesystem of matrix equations A_1X = C_1 and A_3X = C_3 to have a bisymmetric solution, the system ofmatrix equations A_1X = C_1 and A_3XB_3 = C_3 to have a perselfconjugate solution over R with aninvolution and char R≠2, respectively. The representations of such solutions are also presented.Moreover, some auxiliary results on other systems over R are obtained. The previous known results onsome systems of matrix equations are special cases of the new results.
基金
This research is supported by the Natural Science Foundation of China(No.0471085the Natural Science Foundation of Shanghai)
the Development Foundation of Shanghai Educational Committee the Special Funds for Major Specialities of Shanghai Education Co
