摘要
通过应用广义奇异值分解定理 ,得到了矩阵方程ATXA =B的对称正交反对称解存在的一个充要条件 ,导出了通解表达式 ,对给定的矩阵 ,求得了矩阵方程的最佳逼近对称正交反对称解 。
A n×n real P is said to be a symmetric orthogonal-matrix if P T=P and P 2=I.A n×n real X is said to be a symmetric orthogonal anti-symmetric matrix with respect to the orthogonal-matrix P if X T=X=-PXP.By applying the generalized singular value decomposition (GSVD) of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression for the symmetric orthogonal anti-symmetric with a symmetric orthogonal-matrix P solutions of the matrix equation A TXA=B A∈R n×m,B∈R m×m.In addition, in solution set of the equation, the expressions of the optimal approximation solution to the given matrix and of minimum norm solution are derived.
出处
《济南大学学报（自然科学版）》
CAS
2004年第4期343-346,共4页
Journal of University of Jinan(Science and Technology)
基金
国家自然科学基金资助项目 ( 10 1710 3 1)
关键词
矩阵方程
对称正交反对称矩阵
最佳逼近解
matrix equation
symmetric orthogonal anti-symmetric matrices
optimal approximation
