From 38f326c35243942285c43310751025d2c16801dd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 4 Mar 2021 20:30:33 +0100
Subject: Spektraltheorie 1. Teil

---
 vorlesungen/slides/5/bloecke.tex | 141 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 141 insertions(+)
 create mode 100644 vorlesungen/slides/5/bloecke.tex

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

diff --git a/vorlesungen/slides/5/bloecke.tex b/vorlesungen/slides/5/bloecke.tex
new file mode 100644
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+++ b/vorlesungen/slides/5/bloecke.tex
@@ -0,0 +1,141 @@
+%
+% bloecke.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\def\sx{1}
+\def\sy{0.1}
+\def\block#1#2{
+	\fill[color=red] ({#1},{-#1}) rectangle ({#1+#2},{-#1-#2});
+}
+\def\kreuz#1{
+	\draw[color=white,line width=0.1pt] (0,{-#1})--(60,{-#1});
+	\draw[color=white,line width=0.1pt] (#1,0)--(#1,-60);
+}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Blockgrössen aus $\dim\mathcal{K}^k(A)$ ablesen}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.56\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\coordinate (A) at ({1*\sx},{20*\sy});
+\coordinate (B) at ({2*\sx},{(20+15)*\sy});
+\coordinate (C) at ({3*\sx},{(20+15+10)*\sy});
+\coordinate (D) at ({4*\sx},{(20+15+10+8)*\sy});
+\coordinate (E) at ({5*\sx},{(20+15+10+8+5)*\sy});
+\coordinate (F) at ({6*\sx},{(20+15+10+8+5+2)*\sy});
+\fill[color=darkgreen!20] (0,0) -- (A) -- (B) -- (C) -- (D) -- (E) -- (F)
+	-- ({6*\sx},0) -- cycle;
+
+\fill[color=darkgreen!40] (0,0) -- ({1*\sx},0) -- (A) -- cycle;
+\fill[color=darkgreen!40] (A) -- ({2*\sx},{20*\sy}) -- (B) -- cycle;
+\fill[color=darkgreen!40] (B) -- ({3*\sx},{(20+15)*\sy}) -- (C) -- cycle;
+\fill[color=darkgreen!40] (C) -- ({4*\sx},{(20+15+10)*\sy}) -- (D) -- cycle;
+\fill[color=darkgreen!40] (D) -- ({5*\sx},{(20+15+10+8)*\sy}) -- (E) -- cycle;
+\fill[color=darkgreen!40] (E) -- ({6*\sx},{(20+15+10+8+5)*\sy}) -- (F) -- cycle;
+
+\draw[color=darkgreen,line width=1.4pt] (0,0) -- (A) -- (B) -- (C) -- (D) -- (E) -- (F);
+
+\draw[color=gray] (A) -- (0,{20*\sy});
+\draw[color=gray] (B) -- (0,{(20+15)*\sy});
+\draw[color=gray] (C) -- (0,{(20+15+10)*\sy});
+\draw[color=gray] (D) -- (0,{(20+15+10+8)*\sy});
+\draw[color=gray] (E) -- (0,{(20+15+10+8+5)*\sy});
+\draw[color=gray] (F) -- (0,{(20+15+10+8+5+2)*\sy});
+
+\node at ({0.5*\sx},{0.5*20*\sy})
+	[right] {$d_1 = \dim\mathcal{K}^1(A)-\dim\mathcal{K}^0(A)$};
+\node at ({1.5*\sx},{0.5*(20+20+15)*\sy})
+	[right] {$d_2 = \dim\mathcal{K}^2(A)-\dim\mathcal{K}^1(A)$};
+\node at ({2.5*\sx},{0.5*(2*20+2*15+1*10)*\sy}) [right] {$d_3$};
+\node at ({3.5*\sx},{0.5*(2*20+2*15+2*10+8)*\sy}) [right] {$d_4$};
+\node at ({4.5*\sx-0.1},{0.5*(2*20+2*15+2*10+2*8+5)*\sy+0.2}) [below right] {$d_5$};
+\node at ({5.5*\sx},{0.5*(2*20+2*15+2*10+2*8+2*5+2)*\sy+0.1}) [below] {$d_6$};
+
+\fill (A) circle[radius=0.08];
+\fill (B) circle[radius=0.08];
+\fill (C) circle[radius=0.08];
+\fill (D) circle[radius=0.08];
+\fill (E) circle[radius=0.08];
+\fill (F) circle[radius=0.08];
+
+\draw[->] (-0.1,0) -- ({6*\sx+1},0) coordinate[label={$k$}];
+\draw[->] (0,-0.1) -- (0,6.5) coordinate[label={right:$\dim\mathcal{K}^k(A)$}];
+
+\foreach \x in {0,1,...,6}{
+	\draw ({\sx*\x},{-0.05}) -- ({\sx*\x},0.05);
+	\node at ({\sx*\x},{-0.1}) [below] {$\x$};
+}
+
+\node at (0,{60*\sy}) [left] {\llap{$n$}};
+
+\end{tikzpicture}
+\end{center}
+\end{column}
+\begin{column}{0.43\textwidth}
+\vspace{-10pt}
+\begin{center}
+\begin{tabular}{>{$}c<{$}|>{$}r<{$}|>{$}c<{$}|>{$}c<{$}}
+k&d_k&\# M_k(\Bbbk)\text{-Blöcke}&\text{Beispiel}\\
+\hline
+0&  0&        &\\
+1& 20& d_1-d_2&5\\
+2& 15& d_2-d_3&5\\
+3& 10& d_3-d_4&2\\
+4&  8& d_4-d_5&3\\
+5&  5& d_5-d_6&3\\
+6&  2& d_6    &2\\
+\end{tabular}
+\end{center}
+\vspace{-13pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.05]
+\fill[color=gray!40] (0,0) rectangle (60,-60);
+\node[color=white] at (30,-30) [scale=6] {$A$};
+\kreuz{5}
+\kreuz{15}
+\kreuz{21}
+\kreuz{33}
+\kreuz{48}
+\node at (0,-2.5) [left] {$k=1$};
+\node at (60,-2.5) [right] {$5$ Blöcke};
+\node at (0,-10) [left] {$k=2$};
+\node at (60,-10) [right] {$5$ Blöcke};
+\node at (0,-18) [left] {$k=3$};
+\node at (60,-18) [right] {$2$ Blöcke};
+\node at (0,-27) [left] {$k=4$};
+\node at (60,-27) [right] {$3$ Blöcke};
+\node at (0,-40.5) [left] {$k=5$};
+\node at (60,-40.5) [right] {$3$ Blöcke};
+\node at (0,-54) [left] {$k=6$};
+\node at (60,-54) [right] {$2$ Blöcke};
+\block{0}{1}
+\block{1}{1}
+\block{2}{1}
+\block{3}{1}
+\block{4}{1}
+\block{5}{2}
+\block{7}{2}
+\block{9}{2}
+\block{11}{2}
+\block{13}{2}
+\block{15}{3}
+\block{18}{3}
+\block{21}{4}
+\block{25}{4}
+\block{29}{4}
+\block{33}{5}
+\block{38}{5}
+\block{43}{5}
+\block{48}{6}
+\block{54}{6}
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1

