Change colors again and fix typo
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LinAlg2.tex
16
LinAlg2.tex
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@ -39,6 +39,10 @@
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\newcommand\K{\ensuremath{\mathbb{K}}}
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\newcommand\K{\ensuremath{\mathbb{K}}}
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\newcommand\mapsfrom{\rotatebox{180}{$\mapsto$}}
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\newcommand\mapsfrom{\rotatebox{180}{$\mapsto$}}
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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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\theoremstyle{break}
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\theoremstyle{break}
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\theoremseparator{:\smallskip}
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\theoremseparator{:\smallskip}
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\theoremindent=1em
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\theoremindent=1em
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@ -46,7 +50,7 @@
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\theorembodyfont{\normalfont}
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\theorembodyfont{\normalfont}
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\theoreminframepreskip{0em}
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\theoreminframepreskip{0em}
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\theoreminframepostskip{0em}
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\theoreminframepostskip{0em}
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\newtcbox{theoremBox}{colback=Plum!17,colframe=Plum!87,boxsep=0pt,left=7pt,right=7pt,top=7pt,bottom=7pt}
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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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\def\theoremframecommand{\theoremBox}
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\newshadedtheorem{theo}{Theorem}[section]
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\newshadedtheorem{theo}{Theorem}[section]
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@ -55,7 +59,7 @@
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\newshadedtheorem{lemma}[theo]{Lemma}
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\newshadedtheorem{lemma}[theo]{Lemma}
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\newshadedtheorem{korollar}[theo]{Korollar}
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\newshadedtheorem{korollar}[theo]{Korollar}
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\newshadedtheorem{folgerung}[theo]{Folgerung}
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\newshadedtheorem{folgerung}[theo]{Folgerung}
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\newtcbox{definBox}{colback=Cerulean!17,colframe=Cerulean!94,boxsep=0pt,left=7pt,right=7pt,top=7pt,bottom=7pt}
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\newtcbox{definBox}{colback=pastellblau!17,colframe=pastellblau!94,boxsep=0pt,left=7pt,right=7pt,top=7pt,bottom=7pt}
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\def\theoremframecommand{\definBox}
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\def\theoremframecommand{\definBox}
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\newshadedtheorem{defin}[theo]{Definition}
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\newshadedtheorem{defin}[theo]{Definition}
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@ -81,10 +85,6 @@
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\begin{document}
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\begin{document}
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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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\tikzset{%
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\tikzset{%
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-||-/.style={decoration={markings,
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-||-/.style={decoration={markings,
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mark=at position 0.5 with {\draw[thick, -] (-.2,-.2) -- (0, .2);\draw[thick, -] (0, -.2) -- (.2, .2);}},
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mark=at position 0.5 with {\draw[thick, -] (-.2,-.2) -- (0, .2);\draw[thick, -] (0, -.2) -- (.2, .2);}},
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@ -273,7 +273,6 @@ $\pi = (2 3 1), f(X_1, X_2, X_3) = X_1-X_2+X_1X_3 \implies \pi f(X_1, X_2, X_3)
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\end{proof}
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\end{proof}
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\begin{folgerung}
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\begin{folgerung}
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Es gibt genau $\frac12n!$ gerade und $\frac12n!$ ungerade Permutationen in $S_n$
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Es gibt genau $\frac12n!$ gerade und $\frac12n!$ ungerade Permutationen in $S_n$
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\end{folgerung}
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\end{folgerung}
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\begin{proof}
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\begin{proof}
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@ -748,8 +747,7 @@ da obige Matrix aus $M_{ij}$ durch Spaltenadditionen hervorgeht.
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\end{proof}
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\end{proof}
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\begin{folgerung}
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\begin{folgerung}
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Sei $A\in\K^{n\times n}$ invertierbar. Sei $x\in\K^n$ die eindeutige Lösung des linearen Gleichungssystems
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Sei $A\in\K^{n\times n}$ invertierbar. Sei $x\in\K^n$ die eindeutige Lösung des linearen Gleichunssystems
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$Ax=b$. Dann gilt
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$Ax=b$. Dann gilt
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\[
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\[
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x_i= \det(A)^{-1} \det(a_{\_1}, \dots, \underbrace{b}_{i}, \dots, a_{\_n})
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x_i= \det(A)^{-1} \det(a_{\_1}, \dots, \underbrace{b}_{i}, \dots, a_{\_n})
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