实对称矩阵的两个特征值函数及其应用

Two Eigenvalue Functions for Real Symmetric Matrix and Their Applications

针对较高维数矩阵的特征值求解问题,定义实对称矩阵的两个特征值函数,分别用来求解实对称矩阵的前p个最大特征值和最小特征值的和;讨论了这两个特征值函数的性质,列举这两个函数在现代控制理论等领域中的应用;最后给出了特征值函数的求解算法。数值试验表明所定义的特征值函数有效。

To solve the eigenvalue of higher dimensional matrix,two eigenvalue functions for real symmetric matrix were defined in this paper,which were used to solve the sum of the pmaximum eigenvalues and the sum of the pminimum eigenvalues of the matrix respectively.Properties of the two functions were discussed and their applications in control theory were also presented.Numerical algorithms for the above two functions were given.Results of numerical tests indicate that the defined eigenvalue functions are effective.