Fix compilation errors cause by updates
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LinAlg2.tex
18
LinAlg2.tex
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@ -8,14 +8,14 @@
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\usepackage{amssymb}
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\usepackage{marvosym}
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\usepackage{mathtools}
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\usepackage[colorlinks=true, linkcolor=magenta]{hyperref}
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\usepackage{cancel}
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\usepackage[ngerman]{babel}
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\usepackage{harpoon}
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\usetikzlibrary{tikzmark,calc,arrows,arrows.meta,angles,math,decorations.markings}
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\usepackage{pgfplots}
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\usepackage{framed}
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\usepackage[hyperref,amsmath,amsthm,thmmarks,thref,framed]{ntheorem}
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\usepackage[hyperref,amsmath,thmmarks,thref,framed]{ntheorem}
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\usepackage[colorlinks=true, linkcolor=magenta]{hyperref}
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\usepackage{tcolorbox}
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\usepackage{geometry}
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\geometry{a4paper, top=35mm, left=25mm, right=25mm, bottom=30mm}
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@ -39,6 +39,13 @@
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\newcommand\K{\ensuremath{\mathbb{K}}}
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\newcommand\mapsfrom{\rotatebox{180}{$\mapsto$}}
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\theoremsymbol{\ensuremath{\square}}
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\theorembodyfont{\normalfont}
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\theoremheaderfont{\normalfont\it}
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\theoremseparator{.}
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\newtheorem*{proof}{Beweis}
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\qedsymbol{\Lightning}
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\definecolor{pastellblau}{HTML}{5BCFFA}
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\definecolor{pastellrosa}{HTML}{F5ABB9}
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\definecolor{weiss}{HTML}{FFFFFF}
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@ -50,6 +57,7 @@
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\theorembodyfont{\normalfont}
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\theoreminframepreskip{0em}
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\theoreminframepostskip{0em}
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\theoremsymbol{}
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\newtcbox{\theoremBox}{colback=pastellrosa!17,colframe=pastellrosa!87,boxsep=0pt,left=7pt,right=7pt,top=7pt,bottom=7pt}
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\def\theoremframecommand{\theoremBox}
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@ -1095,8 +1103,8 @@ $\le\genfrac{}{}{0pt}{0}{\dim(V)}{n}$, da
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\text{\ref{eq:2.2.10.3}} - \text{\ref{eq:2.2.10.2}}
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& \implies \underbrace{(\lambda_r - \lambda_1)}_{\neq0} \mu_1 v_1 + \cdots +
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\underbrace{(\lambda_r - \lambda_{r-1})}_{\neq0} \mu_{r-1} v_{r-1} = 0 \\
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& \implies v_1, \dots, v_{r-1} \text{ linear abhängig. \Lightning}
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\end{aligned} \]
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& \implies v_1, \dots, v_{r-1} \text{ linear abhängig.}
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\end{aligned} \]\qed
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\end{itemize}
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\end{proof}
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@ -1749,7 +1757,7 @@ Angenommen \(\alpha - \lambda \id: V \to V\) nilpotent. Dann besitzt \(\alpha\)
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Angenommen $\exists l\ge k$ mit $V_{l+1} \neq V_l$. Sei $0\neq v\in V_{l+1} \setminus V_l$
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$\implies 0 = \alpha^{l+1}(v) = \alpha^{k+1}(\alpha^{l-k}(v))$ und $0\neq \alpha^l(v)
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= \alpha^k (\alpha^{l-k}(v)) \implies 0\neq \alpha^{l-k}(v) \in V_{k+1}\setminus V_k$
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\Lightning
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\qed
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\end{proof}
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\begin{defin}
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