From 4614294614e6f6b38e0ca86e77871e75b4c26071 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Tue, 16 Mar 2021 15:48:10 +0100
Subject: add new slides

---
 vorlesungen/slides/2/quotientv.tex | 62 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 vorlesungen/slides/2/quotientv.tex

(limited to 'vorlesungen/slides/2/quotientv.tex')

diff --git a/vorlesungen/slides/2/quotientv.tex b/vorlesungen/slides/2/quotientv.tex
new file mode 100644
index 0000000..dc01f21
--- /dev/null
+++ b/vorlesungen/slides/2/quotientv.tex
@@ -0,0 +1,62 @@
+%
+% quotientv.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkred}{rgb}{0.7,0,0}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Quotient}
+\vspace{-18pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.33\textwidth}
+\begin{block}{Repräsentanten}
+Jeder Unterraum $W\subset V$ mit 
+$W\cap U = \{0\}$
+kann als Menge von Repräsentanten
+für
+\begin{align*}
+V/U
+&=
+\{v+U\;|\;v \in V\}
+\\
+&\simeq W
+\end{align*}
+dienen.
+\end{block}
+\uncover<3->{%
+\begin{block}{Orthogonalraum}
+Mit Skalarprodukt ist
+$W=U^\perp$ eine bevorzugte Wahl
+\end{block}}
+\end{column}
+\begin{column}{0.66\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\only<1>{
+	\node at (0,0)
+	{\includegraphics[width=8.5cm]{../slides/2/images/quotient1.jpg}};
+	\node[color=darkgreen] at (-0.5,0.3) {$v$};
+	\node[color=blue] at (0.7,-1.4) {$w$};
+	\node[color=orange] at (2.7,0.1) {$v+w$};
+	\fill[color=white,opacity=0.5] (3.7,1.0) circle[radius=0.25];
+	\node at (3.7,1.0) {$W$};
+}
+\only<2->{
+	\node at (0,0)
+	{\includegraphics[width=8.5cm]{../slides/2/images/quotient2.jpg}};
+	\node[color=darkgreen] at (-0.75,0.95) {$v$};
+	\node[color=blue] at (0.6,-1.05) {$w$};
+	\node[color=orange] at (2.36,1.05) {$v+w$};
+	\fill[color=white,opacity=0.5] (3.7,2.9) circle[radius=0.25];
+	\node at (3.7,2.9) {$W$};
+}
+\node[color=darkred] at (-3.3,2.6) {$U$};
+\node[color=darkred] at (-2.25,-1.0) {$0$};
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
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