线性矩阵方程组A_1XB_1=D_1,A_2XB_2=D_2的相容性及应用  

CONSISTENCY OF A PAIR OF SIMULTANEOUS LINEAR MATRIX EQUATIONS A1XB1=D1, A2XB2=D2 WITH AN APPLICATION

作　　者：屠文伟[1] 袁永新[1] 

机构地区：[1]华东船舶工业学院基础学科系

出　　处：《曲阜师范大学学报（自然科学版）》1998年第1期51-54,共4页Journal of Qufu Normal University(Natural Science)

摘　　要：给出了联立线性矩阵方程Ａ１ＸＢ１＝Ｄ１，Ａ２ＸＢ２＝Ｄ２的相容性充要条件及通解的显式表示．作为应用，还得出了矩阵方程ＡＸＢ＝Ｄ，ＸＴ＝Ｘ的相容性条件及通解表示．A necessary and sufficient condition is obtained for a pair of simultaneous matrix equations A1XB1=D1, A2XB2=D2 to have a common solution, along with the explicit expression for a general commen solutions when the condition holds. As an application, consistency condition for the symmetric solutions of matrix equation AXB=D is established, and the representation of general solutions is also given. 

关 键 词：矩阵方程 相容性 对称解 通解 线性矩阵方程 

分 类 号：O151.21[理学—数学]