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 A1XB1=D1, A2XB2=D2 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.
出处
《曲阜师范大学学报（自然科学版）》
CAS
1998年第1期51-54,共4页
Journal of Qufu Normal University(Natural Science)
关键词
矩阵方程
相容性
对称解
通解
线性矩阵方程
matrix equation consistency symmetric solution general solutions generalized inverses.
