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authorJoshua Baer <the.baer.joshua@gmail.ch>2021-04-12 21:51:55 +0200
committerJoshua Baer <the.baer.joshua@gmail.ch>2021-04-12 21:51:55 +0200
commit2db90bfe4b174570424c408f04000902411d8755 (patch)
treee297a6274ff748de27257bffd7097c6b362ba12d /buch/chapters/60-gruppen/images/scherungen.tex
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downloadSeminarMatrizen-2db90bfe4b174570424c408f04000902411d8755.tar.gz
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diff --git a/buch/chapters/60-gruppen/images/scherungen.tex b/buch/chapters/60-gruppen/images/scherungen.tex
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--- a/buch/chapters/60-gruppen/images/scherungen.tex
+++ b/buch/chapters/60-gruppen/images/scherungen.tex
@@ -1,157 +1,157 @@
-%
-% scherungen.tex -- template for standalon tikz images
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
-\documentclass[tikz]{standalone}
-\usepackage{amsmath}
-\usepackage{times}
-\usepackage{txfonts}
-\usepackage{pgfplots}
-\usepackage{csvsimple}
-\usetikzlibrary{arrows,intersections,math}
-\begin{document}
-\def\skala{1}
-\begin{tikzpicture}[>=latex,thick,scale=\skala]
-
-\definecolor{blau}{rgb}{0,0.8,1}
-\definecolor{blau}{rgb}{0,0.6,0}
-\def\s{1.1}
-
-\begin{scope}[xshift=-4.6cm]
-
- \fill[color=blue!20] (0,0) rectangle (2,2);
- \fill[color=red!40,opacity=0.5] (0,0) -- (2,\s) -- (2,{2+\s}) -- (0,2)
- -- cycle;
-
- \foreach \x in {-1,...,3}{
- \draw[color=blau] (\x,-1) -- (\x,3);
- \draw[color=blau] (-1,\x) -- (3,\x);
- }
-
- \begin{scope}
- \clip (-1,-1) rectangle (3,3);
- \foreach \x in {-1,...,3}{
- \draw[color=orange] (\x,-1) -- (\x,3);
- \draw[color=orange] (-1,{\x-0.5*\s}) -- (3,{\x+1.5*\s});
- }
- \end{scope}
-
- \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
- \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
-
- \node[color=blue] at (0,2) [above left] {$1$};
- \node[color=blue] at (2,0) [below right] {$1$};
- \draw[->,color=blue] (0,0) -- (2,0);
- \draw[->,color=blue] (0,0) -- (0,2);
-
- \draw[->,color=red] (0,0) -- (2,\s);
- \draw[->,color=red] (0,0) -- (0,2);
-
- \node[color=red] at (2,\s) [below right] {$(1,t)$};
-
- \node at (0,0) [below right] {$O$};
- \node at (1,-1.1) [below] {$\displaystyle
- \begin{aligned}
- M &= \begin{pmatrix}0&0\\1&0 \end{pmatrix}
- \\
- e^{Mt}
- &=
- \begin{pmatrix}1&0\\t&1 \end{pmatrix}
- \end{aligned}
- $};
-\end{scope}
-
-\begin{scope}
- \fill[color=blue!20] (0,0) rectangle (2,2);
- \fill[color=red!40,opacity=0.5] (0,0) -- (2,0) -- ({2+\s},2) -- (\s,2)
- -- cycle;
-
- \foreach \x in {-1,...,3}{
- \draw[color=blau] (\x,-1) -- (\x,3);
- \draw[color=blau] (-1,\x) -- (3,\x);
- }
-
- \begin{scope}
- \clip (-1,-1) rectangle (3,3);
- \foreach \x in {-1,...,3}{
- \draw[color=orange] (-1,\x) -- (3,\x);
- \draw[color=orange] ({\x-0.5*\s},-1) -- ({\x+1.5*\s},3);
- }
- \end{scope}
-
- \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
- \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
-
- \node[color=blue] at (0,2) [above left] {$1$};
- \node[color=blue] at (2,0) [below right] {$1$};
- \draw[->,color=blue] (0,0) -- (2,0);
- \draw[->,color=blue] (0,0) -- (0,2);
-
- \draw[->,color=red] (0,0) -- (2,0);
- \draw[->,color=red] (0,0) -- (\s,2);
-
- \node[color=red] at (\s,2) [above left] {$(t,1)$};
-
- \node at (0,0) [below right] {$O$};
-
- \node at (1,-1.1) [below] {$\displaystyle
- \begin{aligned} N &= \begin{pmatrix}0&1\\0&0 \end{pmatrix}
- \\
- e^{Nt}
- &=
- \begin{pmatrix}1&t\\0&1 \end{pmatrix}
- \end{aligned}
- $};
-\end{scope}
-
-\begin{scope}[xshift=3.6cm,yshift=0cm]
- \def\punkt#1#2{({1.6005*(#1)+0.4114*(#2)},{-0.2057*(#1)+0.5719*(#2)})}
- \fill[color=blue!20] (0,0) rectangle (2,2);
- \fill[color=red!40,opacity=0.5]
- (0,0) -- \punkt{2}{0} -- \punkt{2}{2} -- \punkt{0}{2} -- cycle;
-
- \foreach \x in {0,...,4}{
- \draw[color=blau] (\x,-1) -- (\x,3);
- }
- \foreach \y in {-1,...,3}{
- \draw[color=blau] (0,\y) -- (4,\y);
- }
-
- \begin{scope}
- \clip (-0,-1) rectangle (4,3);
- \foreach \x in {-1,...,6}{
- \draw[color=orange] \punkt{\x}{-3} -- \punkt{\x}{6};
- \draw[color=orange] \punkt{-3}{\x} -- \punkt{6}{\x};
- }
- \end{scope}
-
- \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}];
- \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
-
- \node[color=blue] at (0,2) [above left] {$1$};
- \node[color=blue] at (2,0) [below right] {$1$};
- \draw[->,color=blue] (0,0) -- (2,0);
- \draw[->,color=blue] (0,0) -- (0,2);
-
- \draw[->,color=red] (0,0) -- \punkt{2}{0};
- \draw[->,color=red] (0,0) -- \punkt{0}{2};
-
- \node at (0,0) [below right] {$O$};
-
- \node at (2,-1.1) [below] {$\displaystyle
- \begin{aligned} D &= \begin{pmatrix}0.5&0.4\\-0.2&-0.5 \end{pmatrix}
- \\
- e^{D\cdot 1}
- &=
- \begin{pmatrix}
- 1.6005 & 0.4114\\
- -0.2057 & 0.5719
- \end{pmatrix}
- \end{aligned}
- $};
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%
+% scherungen.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\definecolor{blau}{rgb}{0,0.8,1}
+\definecolor{blau}{rgb}{0,0.6,0}
+\def\s{1.1}
+
+\begin{scope}[xshift=-4.6cm]
+
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5] (0,0) -- (2,\s) -- (2,{2+\s}) -- (0,2)
+ -- cycle;
+
+ \foreach \x in {-1,...,3}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ \draw[color=blau] (-1,\x) -- (3,\x);
+ }
+
+ \begin{scope}
+ \clip (-1,-1) rectangle (3,3);
+ \foreach \x in {-1,...,3}{
+ \draw[color=orange] (\x,-1) -- (\x,3);
+ \draw[color=orange] (-1,{\x-0.5*\s}) -- (3,{\x+1.5*\s});
+ }
+ \end{scope}
+
+ \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- (2,\s);
+ \draw[->,color=red] (0,0) -- (0,2);
+
+ \node[color=red] at (2,\s) [below right] {$(1,t)$};
+
+ \node at (0,0) [below right] {$O$};
+ \node at (1,-1.1) [below] {$\displaystyle
+ \begin{aligned}
+ M &= \begin{pmatrix}0&0\\1&0 \end{pmatrix}
+ \\
+ e^{Mt}
+ &=
+ \begin{pmatrix}1&0\\t&1 \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\begin{scope}
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5] (0,0) -- (2,0) -- ({2+\s},2) -- (\s,2)
+ -- cycle;
+
+ \foreach \x in {-1,...,3}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ \draw[color=blau] (-1,\x) -- (3,\x);
+ }
+
+ \begin{scope}
+ \clip (-1,-1) rectangle (3,3);
+ \foreach \x in {-1,...,3}{
+ \draw[color=orange] (-1,\x) -- (3,\x);
+ \draw[color=orange] ({\x-0.5*\s},-1) -- ({\x+1.5*\s},3);
+ }
+ \end{scope}
+
+ \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- (2,0);
+ \draw[->,color=red] (0,0) -- (\s,2);
+
+ \node[color=red] at (\s,2) [above left] {$(t,1)$};
+
+ \node at (0,0) [below right] {$O$};
+
+ \node at (1,-1.1) [below] {$\displaystyle
+ \begin{aligned} N &= \begin{pmatrix}0&1\\0&0 \end{pmatrix}
+ \\
+ e^{Nt}
+ &=
+ \begin{pmatrix}1&t\\0&1 \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\begin{scope}[xshift=3.6cm,yshift=0cm]
+ \def\punkt#1#2{({1.6005*(#1)+0.4114*(#2)},{-0.2057*(#1)+0.5719*(#2)})}
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5]
+ (0,0) -- \punkt{2}{0} -- \punkt{2}{2} -- \punkt{0}{2} -- cycle;
+
+ \foreach \x in {0,...,4}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ }
+ \foreach \y in {-1,...,3}{
+ \draw[color=blau] (0,\y) -- (4,\y);
+ }
+
+ \begin{scope}
+ \clip (-0,-1) rectangle (4,3);
+ \foreach \x in {-1,...,6}{
+ \draw[color=orange] \punkt{\x}{-3} -- \punkt{\x}{6};
+ \draw[color=orange] \punkt{-3}{\x} -- \punkt{6}{\x};
+ }
+ \end{scope}
+
+ \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- \punkt{2}{0};
+ \draw[->,color=red] (0,0) -- \punkt{0}{2};
+
+ \node at (0,0) [below right] {$O$};
+
+ \node at (2,-1.1) [below] {$\displaystyle
+ \begin{aligned} D &= \begin{pmatrix}0.5&0.4\\-0.2&-0.5 \end{pmatrix}
+ \\
+ e^{D\cdot 1}
+ &=
+ \begin{pmatrix}
+ 1.6005 & 0.4114\\
+ -0.2057 & 0.5719
+ \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+