diff options
Diffstat (limited to 'buch/chapters/40-eigenwerte')
| -rw-r--r-- | buch/chapters/40-eigenwerte/chapter.tex | 1 | ||||
| -rw-r--r-- | buch/chapters/40-eigenwerte/grundlagen.tex | 58 | ||||
| -rw-r--r-- | buch/chapters/40-eigenwerte/images/Makefile | 5 | ||||
| -rw-r--r-- | buch/chapters/40-eigenwerte/images/nilpotent.pdf | bin | 0 -> 14254 bytes | |||
| -rw-r--r-- | buch/chapters/40-eigenwerte/images/nilpotent.tex | 76 | ||||
| -rw-r--r-- | buch/chapters/40-eigenwerte/images/sp.pdf | bin | 24049 -> 24022 bytes |
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 Binary files differnew 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 Binary files differindex 5346e06..d4de984 100644 --- a/buch/chapters/40-eigenwerte/images/sp.pdf +++ b/buch/chapters/40-eigenwerte/images/sp.pdf |