From 2ff283fb087d337f27acacd4d6ec308068199c90 Mon Sep 17 00:00:00 2001 From: Anton Mosich Date: Fri, 22 Apr 2022 11:19:10 +0200 Subject: [PATCH] Fix layout --- LinAlg2.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/LinAlg2.tex b/LinAlg2.tex index c7d6e94..a7ffa24 100644 --- a/LinAlg2.tex +++ b/LinAlg2.tex @@ -1530,7 +1530,7 @@ Angenommen \(\alpha - \lambda \id: V \to V\) nilpotent. Dann besitzt \(\alpha\) $\implies (\alpha - \lambda \id)(v) = (\alpha - \lambda \id)^k (\alpha - \lambda \id)(w) \in \im(\alpha - \lambda \id)^k \checkmark$ \end{itemize} \item Es gilt $\dim(V) = \dim(V_1) + \dim(V_2)$ nach der Dimensionsformel. Es genügt also zu zeigen, dass - $V_1 \cap V_2 = \{0\}$. Sei $v\in V_1 \cap V_2$ + $V_1 \cap V_2 = \{0\}$. \\ Sei $v\in V_1 \cap V_2$ \begin{align*} & \underbrace{\implies}_{v\in V_2} \exists w\in V: v = (\alpha - \lambda \id)^k(w) \\ & \underbrace{\implies}_{v\in V_1} (\alpha - \lambda \id)^{2k}(w) = 0 \\