华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (1): 28-31.

• 应用数学与基础数学 • 上一篇    下一篇

特征空间的扰动

陈建新1,2   

  1. 1.广东工业大学 应用数学学院运筹教研所, 广州 510006; 2.暨南大学 管理学院, 广州 510630
  • 收稿日期:2008-03-11 修回日期:2008-06-10 出版日期:2009-01-25 发布日期:2009-01-25
  • 通讯作者: 陈建新

Perturbations about eigenspaces (Chinese)

CHEN Jian-xin1,2   

  1. 1.Department of Mathematics, Guangdong University Of Technology, Guangzhou 510006, China; 2. Management Science and Engineering of Management School, Jinan University, Guangzhou 510630, China
  • Received:2008-03-11 Revised:2008-06-10 Online:2009-01-25 Published:2009-01-25
  • Contact: CHEN Jian-xin

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摘要： 使用矩阵等式等价变换的方法,~结合~$2$-范数和~$F$-范数的性质及它们与特征值
的关系,~研究了可对角化非奇异矩阵特征空间的扰动上界.~得到了在
~$\eta_{2}=\|{\bm A}^{-\frac{1}{2}}{\bm E}{\bm
A}^{-\frac{1}{2}}\|_{2}<1$~的条件下,~这类矩阵特征 空间~$\|{\rm
sin}\Theta\|_{F}
$~的上界表达式.~对比发现,~所得到的结果是文献[2]定理~$4.1$~的推广.

关键词: 特征空间, Frobenius-范数, 扰动界, 特征空间, Frobenius-范数, 扰动界

Abstract: By using the method of matrix equation equivalent
transformation, combined the properties of $2$-norm and $F$-norm and
their relationship with eigenvalue, this paper dealt with the upper
bound for perturbation of diagonalized non-singular matrix
eigenspaces. Upper bound was obtained for matrix
eigenspace $\|{\rm sin}\Theta\|_{F}$ conditioned by $\eta_{2}=\|{\bm A}^{-\frac{1}{2}}{\bm E}{\bm A}^{-\frac{1}{2}}\|_{2}<1$.
The final theorem is the extension of theorem $4. 1$ in $[2]$.

Key words: Frobenius-norm, perturbation bounds, eigenspace, Frobenius-norm, perturbation bounds

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