线性矩阵方程AXB=C的中心对称解及其最佳逼近  

The Centro-symmetric Solutions of Linear Matrix Equation AXB=C and its Optimal Approximation

作　　者：彭振赟[1] 

机构地区：[1]湖南科技大学数学系,湘潭411201

出　　处：《工程数学学报》2003年第6期60-64,共5页Chinese Journal of Engineering Mathematics

基　　金：湖南省教育厅资助项目(02C025).

摘　　要：利用矩阵的广义异值分解,得到了线性矩阵方程AXB=C有中心对称解的充分必要条件,且有解时,给出了其解的一般表达式。另外。Using the general singular value decomposition of matrices,this paper the necessary and sufficient conditions for the existence of and the expressions for the centro-symmetric soultions of the linear matrix equation AXB=C are given. In addition,in the solution set of corresponding equation,the expression of the optimal approximation soultion to a given in Frobenius norm is derived.

关 键 词：矩阵 矩阵方程 矩阵范数 最佳逼近 

分 类 号：O241.6[理学—计算数学]