From 4d16eab7a381a8379bc139ed2744912683661bab Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Tue, 2 Mar 2021 21:25:06 +0100
Subject: add slides

---
 vorlesungen/slides/5/nilpotent.tex | 176 +++++++++++++++++++++++++++++++++++++
 1 file changed, 176 insertions(+)
 create mode 100644 vorlesungen/slides/5/nilpotent.tex

(limited to 'vorlesungen/slides/5/nilpotent.tex')

diff --git a/vorlesungen/slides/5/nilpotent.tex b/vorlesungen/slides/5/nilpotent.tex
new file mode 100644
index 0000000..9b7ded1
--- /dev/null
+++ b/vorlesungen/slides/5/nilpotent.tex
@@ -0,0 +1,176 @@
+%
+% nilpotent.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\def\feld#1{
+	\fill[color=red!20] (#1,0) rectangle ({#1+1},12);
+}
+\begin{frame}[t]
+\frametitle{$\mathcal{J}^k(f)$ und $\mathcal{K}^k(f)$ für nilpotente Matrizen}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.42\textwidth}
+Matrix mit dem dargestellten Verlauf von
+${\color{red}\dim\mathcal{K}^k(A)}$
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.42]
+
+\only<2->{
+	\feld{0}
+	\feld{1}
+	\feld{2}
+	\feld{3}
+}
+\only<2->{ \feld{4} }
+\only<3->{ \feld{5} }
+\only<2->{ \feld{6} }
+\only<3->{ \feld{7} }
+\only<4->{ \feld{8} }
+\only<5->{ \feld{9} }
+\only<6->{ \feld{10} }
+\only<7->{ \feld{11} }
+
+\only<1>{ \node at (6,0) [below] {$k=0$}; }
+\only<2>{ \node at (6,0) [below] {$k=1$}; }
+\only<3>{ \node at (6,0) [below] {$k=2$}; }
+\only<4>{ \node at (6,0) [below] {$k=3$}; }
+\only<5>{ \node at (6,0) [below] {$k=4$}; }
+\only<6>{ \node at (6,0) [below] {$k=5$}; }
+\only<7>{ \node at (6,0) [below] {$k=6$}; }
+
+\draw (0,0) rectangle (12,12);
+\only<1>{
+	\foreach \x in {1,...,12}{
+		\node at ({\x-0.5},{12-\x+0.5}) {$1$};
+	}
+}
+\only<2->{
+	\foreach \x in {1,...,12}{
+		\node at ({\x-0.5},{12-\x+0.5}) {$0$};
+	}
+}
+\only<2>{
+	\foreach \x in {7,...,11}{
+		\node at ({\x+0.5},{12-\x+0.5}) {$1$};
+	}
+}
+\only<3->{
+	\foreach \x in {7,...,11}{
+		\node at ({\x+0.5},{12-\x+0.5}) {$0$};
+	}
+}
+\only<3>{
+	\foreach \x in {8,...,11}{
+		\node at ({\x+0.5},{13-\x+0.5}) {$1$};
+	}
+}
+\only<4->{
+	\foreach \x in {8,...,11}{
+		\node at ({\x+0.5},{13-\x+0.5}) {$0$};
+	}
+}
+\only<4>{
+	\foreach \x in {9,...,11}{
+		\node at ({\x+0.5},{14-\x+0.5}) {$1$};
+	}
+}
+\only<5->{
+	\foreach \x in {9,...,11}{
+		\node at ({\x+0.5},{14-\x+0.5}) {$0$};
+	}
+}
+\only<5>{
+	\foreach \x in {10,...,11}{
+		\node at ({\x+0.5},{15-\x+0.5}) {$1$};
+	}
+}
+\only<6->{
+	\foreach \x in {10,...,11}{
+		\node at ({\x+0.5},{15-\x+0.5}) {$0$};
+	}
+}
+\only<6>{
+	\foreach \x in {11,...,11}{
+		\node at ({\x+0.5},{16-\x+0.5}) {$1$};
+	}
+}
+\only<7->{
+	\foreach \x in {11,...,11}{
+		\node at ({\x+0.5},{16-\x+0.5}) {$0$};
+	}
+}
+\draw[line width=0.1pt]
+	(0,11) -- (2,11) -- (2,9) -- (4,9) -- (4,6) -- (12,6);
+\draw[line width=0.1pt]
+	(1,12) -- (1,10) -- (3,10) -- (3,8) -- (6,8) -- (6,0);
+\only<2>{
+	\node at (5.5,7.5) {$1$};
+}
+\only<3->{
+	\node at (5.5,7.5) {$0$};
+}
+\end{tikzpicture}
+\end{center}
+\end{column}
+\begin{column}{0.56\textwidth}
+\vspace{-15pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\def\pfad{
+	(0,0) -- (1,3) -- (2,4) -- (3,4.5) -- (4,5) -- (5,5.5) -- (6,6)
+}
+\fill[color=orange!20] \pfad -- (0,6) -- cycle;
+\fill[color=darkgreen!20] \pfad -- (6,0) -- cycle;
+\foreach \y in {0.5,1,...,5.75}{
+	\draw[line width=0.1pt] (0,\y) -- (6,\y);
+}
+\draw[line width=1.4pt] \pfad;
+\draw[->] (-0.1,6) -- (6.5,6); \node at (-0.1,6) [left] {$n$};
+\draw[->] (-0.1,0) -- (6.5,0); \node at (-0.1,0) [left] {$0$};
+\fill (0,0) circle[radius=0.05];
+\fill (1,3) circle[radius=0.05];
+\fill (2,4) circle[radius=0.05];
+\fill (3,4.5) circle[radius=0.05];
+\fill (4,5) circle[radius=0.05];
+\fill (5,5.5) circle[radius=0.05];
+\fill (6,6) circle[radius=0.05];
+\only<1>{
+	\fill[color=red] (0,0) circle[radius=0.08];
+}
+\only<2>{
+	\fill[color=red] (1,3) circle[radius=0.08];
+	\draw[color=red] (0,3) -- (1,3);
+	\node[color=red] at (0,3) [left] {$6$};
+}
+\only<3>{
+	\fill[color=red] (2,4) circle[radius=0.08];
+	\draw[color=red] (0,4) -- (2,4);
+	\node[color=red] at (0,4) [left] {$8$};
+}
+\only<4>{
+	\fill[color=red] (3,4.5) circle[radius=0.08];
+	\draw[color=red] (0,4.5) -- (3,4.5);
+	\node[color=red] at (0,4.5) [left] {$9$};
+}
+\only<5>{
+	\fill[color=red] (4,5.0) circle[radius=0.08];
+	\draw[color=red] (0,5.0) -- (4,5.0);
+	\node[color=red] at (0,5.0) [left] {$10$};
+}
+\only<6>{
+	\fill[color=red] (5,5.5) circle[radius=0.08];
+	\draw[color=red] (0,5.5) -- (5,5.5);
+	\node[color=red] at (0,5.5) [left] {$11$};
+}
+\only<7>{
+	\fill[color=red] (6,6.0) circle[radius=0.08];
+}
+\draw[color=white] (-0.7,0) -- (-0.7,6);
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1

