摘要
利用矩阵的Kronecker乘积,给出了如下两类问题的解的一般形式,同时给出了矩阵方程ATXB-BTXTA=D有解的充分必要条件及有解时其解的一般表达式.问题1给定,,mpmnRBRApnmmRXRD,求使得min||||=--=FDAXBXBATTT.问题2给定XmnSXRX,~求使得XXXXXSX^min^-=-.其中SX是问题1的解集合.
In this paper, using Kronecker product of matrices, the expressions for the solutions of problem I and II are given. In addition, the necessary and sufficient conditions for the solvability of matrix equation ATXB-BTXTA=D is also presented. Problem 1 Given ,,,mmmpmnRDRBRAfind XRnp such that min||||)(=--DAXBXBAXfTTT. Problem 2 Given ,~pnRXfind XSX such that XXXXXSX^min^-=-.where SX is the solution set of Problem I.
出处
《湖南城市学院学报》
2003年第6期63-64,共2页
Journal of Hunan City Univeristy
