move all iamges to separate files

6 files changed, 82 insertions, 58 deletions

diff --git a/buch/chapters/40-eigenwerte/chapter.tex b/buch/chapters/40-eigenwerte/chapter.tex
index e097b8d..e769b38 100644
--- a/buch/chapters/40-eigenwerte/chapter.tex
+++ b/buch/chapters/40-eigenwerte/chapter.tex
@@ -38,6 +38,7 @@ Dies wird in Abschnitt~\ref{buch:section:spektraltheorie} beschrieben.
 \input{chapters/40-eigenwerte/spektraltheorie.tex}
 
 \section*{Übungsaufgaben}
+\rhead{Übungsaufgaben}
 \aufgabetoplevel{chapters/40-eigenwerte/uebungsaufgaben}
 \begin{uebungsaufgaben}
 \uebungsaufgabe{4001}
diff --git a/buch/chapters/40-eigenwerte/grundlagen.tex b/buch/chapters/40-eigenwerte/grundlagen.tex
index 55c3344..dbc19ce 100644
--- a/buch/chapters/40-eigenwerte/grundlagen.tex
+++ b/buch/chapters/40-eigenwerte/grundlagen.tex
@@ -346,63 +346,7 @@ $b_{ij}=0$ für $i+k>j$ und $c_{ij}=0$ für $i+l>j$.
 In der folgenden graphischen Darstellung der Matrizen sind die
 Bereiche, wo die Matrixelemente verschwinden, weiss.
 \begin{center}
-
-\newtcbox{\myboxA}{blank,boxsep=0mm,
-clip upper,minipage,
-width=31.0mm,height=17.0mm,nobeforeafter,
-borderline={0.0pt}{0.0pt}{white},
-}
-
-\begin{tikzpicture}[>=latex,thick]
-
-\def\cx{1.8}
-\def\cy{1.2}
-
-\draw[line width=0.3pt] (-3,2.5) -- (6,2.5);
-
-\begin{scope}[xshift=-4cm]
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (0.5,3) -- (3,0.5) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+0.5*0.5},{\cy+0.5*0.5}) [rotate=-45] {$k$};
-\draw[color=blue,line width=1.4pt] (0,2.5) -- (1.0,2.5);
-\draw[color=red,line width=1.4pt] (1.0,2.5) -- (3,2.5);
-\node at (1,1) {$B$};
-\node at (-0.3,2.5) [left] {$i$};
-\node at (1,2.5) [above right] {$i+k$};
-\end{scope}
-
-\node at (-0.5,1.5) {$\mathstrut\cdot\mathstrut$};
-
-\begin{scope}
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (1.0,3) -- (3,1.0) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+1.0*0.5},{\cy+1.0*0.5}) [rotate=-45] {$l$};
-\draw[color=red,line width=1.4pt] (2,3)--(2,2);
-\draw[color=blue,line width=1.4pt] (2,2)--(2,0);
-\node at (1,1) {$C$};
-\node at (2,3) [above] {$j$};
-\node at (2,2) [above right] {$j-l$};
-\end{scope}
-
-\node at (3.5,1.5) {$\mathstrut=\mathstrut$};
-
-\begin{scope}[xshift=4cm]
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (1.5,3) -- (3,1.5) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+1.5*0.5},{\cy+1.5*0.5}) [rotate=-45] {$k+l$};
-\fill[color=red!50!blue] (2,2.5) circle[radius=0.1];
-\draw[line width=0.3pt] (2,3) -- (2,2.5);
-\node at (2,3) [above] {$j$};
-\node at (1,1) {$D$};
-\end{scope}
-
-\end{tikzpicture}
+\includegraphics{chapters/40-eigenwerte/images/nilpotent.pdf}
 \end{center}
 Bei der Berechnung des Elementes $d_{ij}$ wird die Zeile $i$ von $B$
 mit der Spalte $j$ von $C$ multipliziert.
diff --git a/buch/chapters/40-eigenwerte/images/Makefile b/buch/chapters/40-eigenwerte/images/Makefile
index 5915d30..db00dac 100644
--- a/buch/chapters/40-eigenwerte/images/Makefile
+++ b/buch/chapters/40-eigenwerte/images/Makefile
@@ -3,7 +3,7 @@
 #
 # (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
 #
-all:	sp.pdf 
+all:	sp.pdf   nilpotent.pdf
 
 sp.pdf:	sp.tex sppaths.tex
 	pdflatex sp.tex
@@ -11,3 +11,6 @@ sp.pdf:	sp.tex sppaths.tex
 sppaths.tex:	spbeispiel.m
 	octave spbeispiel.m
 
+nilpotent.pdf:	nilpotent.tex
+	pdflatex nilpotent.tex
+
diff --git a/buch/chapters/40-eigenwerte/images/nilpotent.pdf b/buch/chapters/40-eigenwerte/images/nilpotent.pdf
new file mode 100644
index 0000000..2106697
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/nilpotent.pdf
diff --git a/buch/chapters/40-eigenwerte/images/nilpotent.tex b/buch/chapters/40-eigenwerte/images/nilpotent.tex
new file mode 100644
index 0000000..1e6cd79
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/nilpotent.tex
@@ -0,0 +1,76 @@
+%
+% nilpotent.tex -- Produkt nilpotenter Matrizen
+%
+% (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}
+\usepackage[many]{tcolorbox}
+
+\begin{document}
+\def\skala{1}
+
+\newtcbox{\myboxA}{blank,boxsep=0mm,
+clip upper,minipage,
+width=31.0mm,height=17.0mm,nobeforeafter,
+borderline={0.0pt}{0.0pt}{white},
+}
+
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\cx{1.8}
+\def\cy{1.2}
+
+\draw[line width=0.3pt] (-3,2.5) -- (6,2.5);
+
+\begin{scope}[xshift=-4cm]
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (0.5,3) -- (3,0.5) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+0.5*0.5},{\cy+0.5*0.5}) [rotate=-45] {$k$};
+\draw[color=blue,line width=1.4pt] (0,2.5) -- (1.0,2.5);
+\draw[color=red,line width=1.4pt] (1.0,2.5) -- (3,2.5);
+\node at (1,1) {$B$};
+\node at (-0.3,2.5) [left] {$i$};
+\node at (1,2.5) [above right] {$i+k$};
+\end{scope}
+
+\node at (-0.5,1.5) {$\mathstrut\cdot\mathstrut$};
+
+\begin{scope}
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (1.0,3) -- (3,1.0) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+1.0*0.5},{\cy+1.0*0.5}) [rotate=-45] {$l$};
+\draw[color=red,line width=1.4pt] (2,3)--(2,2);
+\draw[color=blue,line width=1.4pt] (2,2)--(2,0);
+\node at (1,1) {$C$};
+\node at (2,3) [above] {$j$};
+\node at (2,2) [above right] {$j-l$};
+\end{scope}
+
+\node at (3.5,1.5) {$\mathstrut=\mathstrut$};
+
+\begin{scope}[xshift=4cm]
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (1.5,3) -- (3,1.5) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+1.5*0.5},{\cy+1.5*0.5}) [rotate=-45] {$k+l$};
+\fill[color=red!50!blue] (2,2.5) circle[radius=0.1];
+\draw[line width=0.3pt] (2,3) -- (2,2.5);
+\node at (2,3) [above] {$j$};
+\node at (1,1) {$D$};
+\end{scope}
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/chapters/40-eigenwerte/images/sp.pdf b/buch/chapters/40-eigenwerte/images/sp.pdf
index 5346e06..d4de984 100644
--- a/buch/chapters/40-eigenwerte/images/sp.pdf
+++ b/buch/chapters/40-eigenwerte/images/sp.pdf