Visualisierungen für Perron-Frobenius-Theorie

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diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex
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+++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex
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+%
+% vergleich.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{5}
+\def\hoehe{5}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=10cm]{vergleich.jpg}};
+
+\node at (-1.3,-4.8) [right] {$x_1$};
+\node[opacity=0.5] at (1.9,-0.9) [right] {$x_2$};
+\node at (-4.6,4.7) [right] {$x_3$};
+
+\node at (-3.2,2.6) [above] {$u$};
+\node at (-3.5,-0.7) [below left] {$v$};
+\node at (-1,2.8) [above] {$Au$};
+\node at (-2.6,-0.5) [below] {$Av$};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw                            (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\end{tikzpicture}
+
+\end{document}
+