关于矩阵方程AX=B,XC=D及AXB=D的对称正定解  

On the Symmetric Positive Definite Solutions of Matrix Equation AX=B, XC=D and AXB=D

作　　者：袁永新[1] 

机构地区：[1]华东船舶工业学院基础学科系,江苏镇江212003

出　　处：《华东船舶工业学院学报》2000年第6期9-12,共4页Journal of East China Shipbuilding Institute(Natural Science Edition)

摘　　要：借助于矩阵的奇异值分解及矩阵的广义逆 ,给出了矩阵方程AX =B ,XC =D及AXB =D有对称正定解的充分必要条件 ,并在有解的情况下 ,给出了通解的显式表示。A necessary and sufficient condition for matrix equations AX=B, XC=D and AXB=D to have symmetric positive definite solutions is obtained by using SVD and generalized inverses of matrices, and the explicit representation of general solutions is also given.

关 键 词：矩阵方程 对称正定阵 通解 对称正定解 

分 类 号：O151.21[理学—数学]