Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (1): 28-31.

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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

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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