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proof 2.57 underbrace corrected

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JosuaKugler
2020-05-22 09:21:31 +02:00
parent f2aeceb5ae
commit 80a8fc0a35
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@@ -45,7 +45,7 @@
\begin{proof} \begin{proof}
Es ist $\tilde A = \tilde A + A - A = (\tilde A - A) + A = A Es ist $\tilde A = \tilde A + A - A = (\tilde A - A) + A = A
(\underbrace{A^{-1} (\tilde A - A) + \mathbb{I}}_{=:B})$. Damit folgt (\underbrace{A^{-1} (\tilde A - A) }_{=:B} + \mathbb{I})$. Damit folgt
$\Vert B \Vert = \Vert A^{-1} (\tilde A - A) \Vert \le \Vert A^{-1} \Vert \cdot \Vert \tilde A $\Vert B \Vert = \Vert A^{-1} (\tilde A - A) \Vert \le \Vert A^{-1} \Vert \cdot \Vert \tilde A
- A \Vert < 1$. - A \Vert < 1$.
Mit \ref{lemma:stoerung} folgt $\mathbb{I} + A^{-1}(\tilde A - A)$ regulär. Da Mit \ref{lemma:stoerung} folgt $\mathbb{I} + A^{-1}(\tilde A - A)$ regulär. Da
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