吉林大学学报（理学版）Issue(2)：206-212,7.DOI:10.13413/j.cnki.jdxblxb.2015.02.10
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
摘要
Abstract
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Key words
matrix equations/symmetric matrix/anti-symmetric matrix/optimal approximation/canonical correlation decomposition (CCD)分类
数理科学引用本文复制引用
郭丽杰,周硕..一类矩阵方程组 AX =B，XD =E的对称解与反对称解[J].吉林大学学报（理学版）,2015,(2):206-212,7.基金项目
国家自然科学基金(批准号:11072085)和吉林省自然科学基金(批准号:2011 1 5 180) （批准号:11072085）
