From e2737868b67b183152c4436ececf12e68b5a145b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 21 Mar 2021 20:37:06 +0100
Subject: new slides

---
 vorlesungen/slides/5/kernbildintro.tex | 89 ++++++++++++++++++++++++++++++++++
 1 file changed, 89 insertions(+)
 create mode 100644 vorlesungen/slides/5/kernbildintro.tex

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

diff --git a/vorlesungen/slides/5/kernbildintro.tex b/vorlesungen/slides/5/kernbildintro.tex
new file mode 100644
index 0000000..9fd7849
--- /dev/null
+++ b/vorlesungen/slides/5/kernbildintro.tex
@@ -0,0 +1,89 @@
+%
+% kernbildintro.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+
+\definecolor{grueneins}{rgb}{0.0,0.4,0.0}
+\definecolor{gruenzwei}{rgb}{0.0,0.4,0.8}
+\definecolor{orangeeins}{rgb}{1.0,0.6,0.0}
+\definecolor{orangezwei}{rgb}{0.8,0.0,0.4}
+
+\begin{frame}[t]
+\frametitle{Bilder und Kerne}
+\vspace{-15pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\begin{scope}[xshift=-3.4cm]
+
+\only<1>{
+\node at (0,0) {\includegraphics[width=6.6cm]{../slides/5/beispiele/leer.jpg}};
+}
+\only<2-3>{
+\node at (0,0) {\includegraphics[width=6.6cm]{../slides/5/beispiele/bild1.jpg}};
+}
+\uncover<4->{
+\node at (0,0) {\includegraphics[width=6.6cm]{../slides/5/beispiele/bild2.jpg}};
+}
+\uncover<2->{
+	\fill[color=white,opacity=0.7]  (0.1,2.18) rectangle (4,2.64);
+	\node[color=orangeeins] at (0,2.4) [right]
+		{$\operatorname{im} A = \{Av\;|v\in\mathbb{R}^n\}$};
+}
+\uncover<4->{
+	\node[color=orangezwei] at (4,0.7) [left]
+		{$\operatorname{im} A^2 = \{A^2v\;|v\in\mathbb{R}^n\}$};
+}
+\end{scope}
+
+\begin{scope}[xshift=3.4cm]
+
+\uncover<2->{
+\fill[color=orangeeins!40] (-1,0.5) rectangle (1.8,2);
+}
+\uncover<4->{
+\fill[color=orangezwei!40] (-1.1,-1.7) rectangle (-0.,-0.3);
+}
+
+\node at (0,0) {\begin{minipage}{6cm}
+\begin{align*}
+A&={\scriptstyle\begin{pmatrix*}[r]
+  -0.979& -0.142&  0.917\\
+  -0.260& -0.643&  1.069\\
+  -0.285& -0.449&  0.823
+\end{pmatrix*}}
+\\
+\operatorname{Rang}A&=2
+\\
+\uncover<3->{
+A^2&={\scriptstyle\begin{pmatrix*}[r]
+   0.734& -0.181& -0.295\\
+   0.118& -0.029& -0.047\\
+   0.161& -0.039& -0.065
+\end{pmatrix*}}}\\
+\uncover<3->{
+\operatorname{Rang}A^2&=1}
+\end{align*}
+\end{minipage}};
+
+\only<5>{
+\node at (0,0) {\includegraphics[width=6.6cm]{../slides/5/beispiele/kern1.jpg}};
+}
+
+\uncover<6->{
+\node at (0,0) {\includegraphics[width=6.6cm]{../slides/5/beispiele/kern2.jpg}};
+\node[color=gruenzwei] at (-1.35,-3.0) [right] {$\ker A^2 = \{v\;|\; A^2v=0\}$};
+}
+
+\uncover<5->{
+\node[color=grueneins] at (-0.9,3.1) [right] {$\ker A = \{v\;|\; Av=0\}$};
+}
+
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+\end{frame}
+\egroup
-- 
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