矩阵方程AXB=D的对称解的通式  

The General Expressions of Symmetric Solutions of Matrix Equation AXB=D

作　　者：吴筑筑[1] 

机构地区：[1]韶关学院计算机系,广东韶关512005

出　　处：《韶关学院学报》2002年第3期6-10,共5页Journal of Shaoguan University

摘　　要：利用广义逆矩阵给出矩阵方程AXB =D有对称解的充要条件以及对称解的通式 .该通解表为方程的一个对称特解及AXB=O 的对称通解之和 当B=I时得到方程AX=DThe necessary and sufficient conditions for the existence of the symmetric solutions of the equation AXB=D and the general expressions of the symmetric solutions are presented by using the generalized inverse matrices.The general solutions are expressed as the sum of the special symmetric solution of AXB=D and the general symmetric solutions of AXB=O.When B=I,the expressions become the general symmetric solutions of AX=D.

关 键 词：矩阵方程 对称矩阵 广义逆矩阵 

分 类 号：O15[理学—数学] 0241[理学—基础数学]