可对称化矩阵特征值的Wielandt型扰动上界

Wielandt Type Perturbation Upper Bound of Eigenvalues of Symmetrizable Matrix

设A∈Cn×n,B=A+E为其扰动矩阵,A、B的特征值分别为λ(A)={λk},λ(B)={μk}.关于特征值的传统误差界是估计 |μi-λi|.利用矩阵的奇异值分解得到了可对称化矩阵特征值的Wielandt型绝对扰动上界,改进了以往的结果.

If A∈Cn×n,B=A＋E is its perturbation matrix,the eigenvalues of A,B are respectively λ（A）={λk},λ（B）={μk}.The traditional error bound of eigenvalues is estimation ｜μi-λi｜.utilizes the decomposition of matrix,obtains the Wielandt type absolute perturbation upper bound of eigenvalues of symmetrizable matrix,improves the former results.