可对角化矩阵的特征值与特征空间的扰动
Perturbation Bounds of Eigenvalues and Eigenspaces for Diagonalizable Matrices

矩阵特征值和特征空间的计算是数值代数的重要课题之一,在科学工程计算等领域有重要的作用. 而特征值与特征空间的扰动分析是有关特征值数值分析的一个重要研究方向,它的经典结果分别是特征值扰动的Hoffman-Wielandt定理和特征空间的sin θ定理. 文中所考虑的是可对角化矩阵的乘法与加法扰动下的特征值与特征空间的组合扰动分析，给出了组合扰动界,所得到的结果推广了Hermite矩阵的组合扰动的相关结果. 另一方面，从新得到的结果可以分别导出有关特征值和特征空间的扰动界.
： The computation for eigenvalues and eigenspaces is one of the important research fields in numerical algebra, and it plays an important role in scientific Engineering computations. The perturbation analysis for eigenvalues and eigenspaces is one of the significant topics in the numerical analysis in eigenvalue computing. The classical perturbation results are the Hoffman-Wielandt theorem for eigenvalue perturbation and the sinθ for the eigenspace. In this paper, the combined perturbation analysis for the matrix and it's perturbed matrix being diagonalizable matrices under the additive and the multiplicative perturbation are considered, and their combined perturbation bounds are given, respectively, which extend the corresponding combined perturbation result for the Hermitian matrix case. On the other hand, the eigenvalue perturbation bound and the eigenspace perturbation bound can be derived from the new bounds, respectively