一类矩阵方程组AX=B,XD=E的对称解与反对称解  

Symmetric Solution and Anti-symmetric Solution for a Class of Matrix Equations AX=B,XD=E

作　　者：郭丽杰[1] 周硕[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《吉林大学学报（理学版）》2015年第2期206-212,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11072085);吉林省自然科学基金(批准号:201115180)

摘　　要：考虑矩阵方程组AX=B,XD=E的对称解与反对称解,利用对称(反对称)矩阵的性质和矩阵对的标准相关分解(CCD),给出了矩阵方程组对称解(反对称解)存在的充分必要条件及解的一般表达式,并讨论了对任意给定矩阵的最佳逼近问题.The symmetric solution and the anti-symmetric solution of matrix equations AX=B,XD=E were considered.Based on the special properties of symmetric（anti-symmetric）matrices and the canonical correlation decomposition（CCD）of a pair of matrices,the necessary and sufficient conditions for the solvability and the general expression of the symmetric solution（anti-symmetric solution）were obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set was solved.

关 键 词：矩阵方程组 对称矩阵 反对称矩阵 最佳逼近 标准相关分解 

分 类 号：O241.6[理学—计算数学]