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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~$\eta_{2}=\|{\bm A}^{-\frac{1}{2}}{\bm E}{\bmA}^{-\frac{1}{2}}\|_{2}1$~的条件下,~这类矩阵特征 空间~$\|{\rmsin}\Theta\|_{F}$~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.
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关键词:
- 特征空间 /
- Frobenius-范数 /
- 扰动界
Abstract: By using the method of matrix equation equivalenttransformation, combined the properties of $2$-norm and $F$-norm andtheir relationship with eigenvalue, this paper dealt with the upperbound for perturbation of diagonalized non-singular matrixeigenspaces. 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:
- eigenspaceFrobenius-normperturbation bounds /
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