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/zerlegung.tex | 44 ++++++++++++++++++++++++++++++++------
 1 file changed, 38 insertions(+), 6 deletions(-)

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

diff --git a/vorlesungen/slides/5/zerlegung.tex b/vorlesungen/slides/5/zerlegung.tex
index 9c20c60..a734d69 100644
--- a/vorlesungen/slides/5/zerlegung.tex
+++ b/vorlesungen/slides/5/zerlegung.tex
@@ -14,27 +14,48 @@
 \begin{column}{0.48\textwidth}
 \begin{center}
 \begin{tikzpicture}[>=latex,thick,scale=0.38]
+\uncover<2->{
 \fill[color=blue!20] (0,11) rectangle (4,15);
 \fill[color=red!20] (4,0) rectangle (15,11);
+}
+\uncover<3->{
 \fill[color=red!40] (9,0) rectangle (15,6);
 \fill[color=blue!40,opacity=0.5] (4,6) rectangle (9,11);
+}
+\uncover<4->{
 \fill[color=blue!40,opacity=0.5] (9,3) rectangle (12,6);
 \fill[color=blue!40,opacity=0.5] (12,0) rectangle (15,3);
+}
+
+\uncover<2->{
 \draw[line width=0.1pt] (0,11) -- (15,11);
-\draw[line width=0.1pt] (0,6) -- (15,6);
-\draw[line width=0.1pt] (0,3) -- (15,3);
 \draw[line width=0.1pt] (4,0) -- (4,15);
+}
+
+\uncover<3->{
+\draw[line width=0.1pt] (0,6) -- (15,6);
 \draw[line width=0.1pt] (9,0) -- (9,15);
+}
+
+\uncover<4->{
+\draw[line width=0.1pt] (0,3) -- (15,3);
 \draw[line width=0.1pt] (12,0) -- (12,15);
+}
 \draw (0,0) rectangle (15,15);
+\uncover<2->{
 \node[color=darkgreen] at (2,15) [above] {$\mathcal{E}_{\lambda_1}$};
-\node at (7,15) [above] {$\mathcal{E}_{\lambda_2}$};
-\node at (10.5,15) [above] {$\mathcal{E}_{\lambda_3}$};
-\node at (13.5,15) [above] {$\mathcal{E}_{\lambda_4}$};
 \node[color=darkgreen] at (0,13) [above,rotate=90] {$\mathcal{K}(f-\lambda_1)$};
 \node at (2,13) {$f_{|\mathcal{E}_{\lambda_1}}$};
+}
+\uncover<3->{
+\node at (7,15) [above] {$\mathcal{E}_{\lambda_2}$};
 \node at (7,8.5) {$(f_1)_{|\mathcal{E}_{\lambda_2}}$};
+}
+\uncover<4->{
+\node at (10.5,15) [above] {$\mathcal{E}_{\lambda_3}$};
+\node at (13.5,15) [above] {$\mathcal{E}_{\lambda_4}$};
 \node at (10.5,4.5) {$(f_2)_{|\mathcal{E}_{\lambda_3}}$};
+}
 \end{tikzpicture}
 \end{center}
 \end{column}
@@ -42,30 +63,41 @@
 \begin{block}{Iteration}
 $\Lambda=\{\lambda_1,\dots,\lambda_s\}$ Eigenwerte
 \begin{align*}
+\uncover<2->{
 V
 &=
 \mathcal{K}(f-\lambda_1)
 \oplus
 \raisebox{-22pt}{\smash{\rlap{\tikz{\fill[color=red!20] (0,0) rectangle (1.83,1.1);}}}}
 \underbrace{\mathcal{J}(f-\lambda_1)}_{\displaystyle=V_1}
+}
 \\[-15pt]
+\uncover<2->{
 f_1 &= f_{|V_1}
+}
 \\[10pt]
+\uncover<3->{
 V_1
 &=
 \mathcal{K}(f_1-\lambda_2)
 \oplus
 \raisebox{-22pt}{\smash{\rlap{\tikz{\fill[color=red!40] (0,0) rectangle (1.9,1.1);}}}}
 \underbrace{\mathcal{J}(f_1-\lambda_2)}_{\displaystyle=V_2}
+}
 \\[-15pt]
+\uncover<3->{
 f_1 &= f_{|V_1}
+}
 \\
+\uncover<4->{
 &\phantom{0}\vdots
+}
 \end{align*}
+\uncover<5->{%
 $\Rightarrow$ $f$ hat {\color{blue}Blockdiagonalform} für die Zerlegung
 \begin{align*}
 V&=\bigoplus_{\lambda\in\Lambda} \mathcal{E}_{\lambda}
-\end{align*}
+\end{align*}}
 \end{block}
 \end{column}
 \end{columns}
-- 
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