Hermite矩阵特征空间的扰动界

Perturbation Bounds of Eigenspaces for Hermitian Matrices

矩阵的特征值在各个领域中都有着广泛的应用,其中Hermite矩阵的特征值问题占有重要地位,尤其是在概率论、控制优化、经济管理等诸多领域都有重要应用.在实际计算过程中往往存在误差,使特征值的计算产生扰动.本文借助谱分解定理和奇异值理论以及矩阵理论中的相关性质来研究Hermite矩阵的特征空间的扰动,利用Rayleigh商来界定Hermite矩阵特征空间的扰动界,给出了两个新的扰动界.

The eigenvalues of matrix is widely used in various fields,and the problems of the eigenvalues on Hermitian matrix,which play an important role,has been applied especially in probability theory,control and optimization,economic management.In the practical calculation,due to errors,we usually get the approximate value,namely,the eigenvalue of matrix has perturbation.In this paper,by means of SVD Theorem,the related theory in singularvalue and Matrix,we discuss perturbation bounds of Hermitian matrices,and get the perturbation bound of the Hermitian matrix's subeigenspace by Rayleigh Quotient,and two new perturbation bounds are presented,which improve some previous corresponding results in some sense.