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(\tilde A - A) + \mathbb{I}}_{=:B})$. Damit folgt + (\underbrace{A^{-1} (\tilde A - A) }_{=:B} + \mathbb{I})$. Damit folgt $\Vert B \Vert = \Vert A^{-1} (\tilde A - A) \Vert \le \Vert A^{-1} \Vert \cdot \Vert \tilde A - A \Vert < 1$. Mit \ref{lemma:stoerung} folgt $\mathbb{I} + A^{-1}(\tilde A - A)$ regulär. 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