一般矩阵特征值新的相对扰动界

New bounds of relative perturbation for eigenvalues of arbitrary matrices

利用矩阵的约当分解和矩阵的Schur三角分解及矩阵的计算技巧,深入探讨了任意矩阵特征值的相对扰动问题。在矩阵特征值绝对扰动的基础上,得到了全新的任意矩阵特征值的相对扰动上界,并且所得结果推广了原有的结论。

Using the Jordan decomposition and Schur decomposition of matrix, we investigated the perturbationfor eigenvalues of matrices. Base on the absolute perturbation of matices, we obtained the new upper bounds ofrelative perturbation of arbitrary matrices. We get the result, which extend the original theorem.