Spektraltheorie 1. Teil

1 files changed, 57 insertions, 5 deletions

diff --git a/vorlesungen/slides/5/folgerungen.tex b/vorlesungen/slides/5/folgerungen.tex
index a1fa6bf..4a8dbe6 100644
--- a/vorlesungen/slides/5/folgerungen.tex
+++ b/vorlesungen/slides/5/folgerungen.tex
@@ -3,10 +3,14 @@
 %
 % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 %
+\bgroup
+\def\sx{1}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
 \begin{frame}[t]
 \frametitle{Folgerungen}
+\vspace{-10pt}
 \begin{columns}[t]
-\begin{column}{0.48\textwidth}
+\begin{column}{0.30\textwidth}
 \begin{block}{Zunahme}
 Für alle $k<l$ gilt
 \begin{align*}
@@ -23,10 +27,58 @@ Für $k\ge l$ gilt
 Ausserdem ist $l\le n$
 \end{block}
 \end{column}
-\begin{column}{0.48\textwidth}
-\begin{proof}[Beweis]
-XXX
-\end{proof}
+\begin{column}{0.66\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\def\pfad{
+	({0*\sx},6) --
+	({1*\sx},4.5) --
+	({2*\sx},3.5) --
+	({3*\sx},2.9) --
+	({4*\sx},2.6) --
+	({5*\sx},2.4) --
+	({6*\sx},2.4)
+}
+
+\fill[color=orange!20] \pfad -- ({6*\sx},0) -- (0,0) -- cycle;
+\fill[color=darkgreen!20] \pfad -- ({6*\sx},6) -- cycle;
+\fill[color=orange!40] ({5*\sx},0) rectangle ({6*\sx},2.4);
+\fill[color=darkgreen!40] ({5*\sx},6) rectangle ({6*\sx},2.4);
+
+\draw[color=darkgreen,line width=2pt] ({3*\sx},6) -- ({3*\sx},2.9);
+\node[color=darkgreen] at ({3*\sx},4.45) [rotate=90,above] {$\dim\mathcal{K}^k(A)$};
+\draw[color=orange,line width=2pt] ({3*\sx},0) -- ({3*\sx},2.9);
+\node[color=orange] at ({3*\sx},1.45) [rotate=90,above] {$\dim\mathcal{J}^k(A)$};
+
+\node[color=orange] at ({5.5*\sx},1.2) [rotate=90] {bijektiv};
+\node[color=darkgreen] at ({5.5*\sx},4.2) [rotate=90] {konstant};
+
+\fill ({0*\sx},6) circle[radius=0.08];
+\fill ({1*\sx},4.5) circle[radius=0.08];
+\fill ({2*\sx},3.5) circle[radius=0.08];
+\fill ({3*\sx},2.9) circle[radius=0.08];
+\fill ({4*\sx},2.6) circle[radius=0.08];
+\fill ({5*\sx},2.4) circle[radius=0.08];
+\fill ({6*\sx},2.4) circle[radius=0.08];
+
+\draw \pfad;
+
+\draw[->] (-0.1,0) -- ({6*\sx+0.5},0) coordinate[label={$k$}];
+\draw[->] (-0.1,6) -- ({6*\sx+0.5},6);
+
+\foreach \x in {0,...,6}{
+	\draw (\x,-0.05) -- (\x,0.05);
+}
+\foreach \x in {0,...,3}{
+	\node at ({\x*\sx},-0.05) [below] {$\x$};
+}
+\node at ({4*\sx},-0.05) [below] {$\dots\mathstrut$};
+\node at ({5*\sx},-0.05) [below] {$l$};
+\node at ({6*\sx},-0.05) [below] {$l+1$};
+
+\end{tikzpicture}
+\end{center}
 \end{column}
 \end{columns}
 \end{frame}
+\egroup