摘要
提出了正交矩阵的逆特征值问题,讨论了该问题有解的充要条件,并给出了解的表达式.同时考虑了解集合对给定矩阵的最佳逼近问题.最后,当该问题无解时,讨论了它的最小二乘解.数值实例说明理论是正确的,算法是可行的.
The inverse eigenvalue problem of orthogonal matrices was firstly considered. The neccesary and sufficent condions of solvablity for the problem were derived and the expression of general solution was given. Then the best approximation to any given matrix was also considered and the solutions were obtained. Finally when the solvablity condions were not meeted, we investigated the least square problem,and we illustrated the main theories and algorithm with numerical examples.
出处
《湖南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2005年第1期116-120,共5页
Journal of Hunan University:Natural Sciences
基金
国家自然科学基金资助项目(10171031)
关键词
正交矩阵
逆特征值问题
最佳逼近
最小二乘解
orthogonal matrices
inverse eigenvalue problem
the best approximation
optimal approximation
least-squares solution
