可对称化矩阵特征值的任意扰动

Arbitrary Perturbation Bounds on Diagonalizable Matrix

针对可对称化矩阵,研究了可对称化矩阵特征值的任意扰动和实任意扰动。从Schur分解入手,利用矩阵可对角化的性质,通过矩阵等式的恒等变形,得到了可对角化矩阵关于F-范数和Q-范数的任意扰动界。

In this paper, to symmetrical matrix (diagonalizable matrix), we have studied arbitrary perturbation and real arbitrary perturbation of it (with real eigenvalue arbitrary perturbation). It is started with to resolve from everybody known very well Schur decomposition, utilizing matrix that can be diagonalizable and identically equal through matrix equality out of shape, receiving perturbation bounds of diagonalizable matrix about F-norm and Q-norm.