From 69c5a77e6f008330327f2697f9c77cea6f2e1c3a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@othello.ch>
Date: Tue, 16 Feb 2021 22:05:38 +0100
Subject: chapter 1 slides

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

(limited to 'vorlesungen/slides/1/dreieck.tex')

diff --git a/vorlesungen/slides/1/dreieck.tex b/vorlesungen/slides/1/dreieck.tex
new file mode 100644
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--- /dev/null
+++ b/vorlesungen/slides/1/dreieck.tex
@@ -0,0 +1,62 @@
+%
+% dreieck.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Dreiecksmatrizen}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.31\textwidth}
+\begin{block}{Dreiecksmatrix}
+\begin{align*}
+R&=
+\begin{pmatrix}
+*&*&*&\dots&*\\
+0&*&*&\dots&*\\
+0&0&*&\dots&*\\
+\vdots&\vdots&\vdots&\ddots&\vdots\\
+0&0&0&\dots&*
+\end{pmatrix}
+\\
+U&=
+\begin{pmatrix}
+1&*&*&\dots&*\\
+0&1&*&\dots&*\\
+0&0&1&\dots&*\\
+\vdots&\vdots&\vdots&\ddots&\vdots\\
+0&0&0&\dots&1
+\end{pmatrix}
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.31\textwidth}
+\begin{block}{Nilpotente Matrix}
+\[
+N=
+\begin{pmatrix}
+*&*&*&\dots&*\\
+0&*&*&\dots&*\\
+0&0&*&\dots&*\\
+\vdots&\vdots&\vdots&\ddots&\vdots\\
+0&0&0&\dots&*
+\end{pmatrix}
+\]
+$\Rightarrow N^n=0$
+\end{block}
+\end{column}
+\begin{column}{0.31\textwidth}
+\begin{block}{Jordan-Matrix}
+\[
+J_\lambda=\begin{pmatrix}
+\lambda&1&0&\dots&0\\
+0&\lambda&1&\dots&0\\
+0&0&\lambda&\dots&0\\
+\vdots&\vdots&\vdots&\ddots&\vdots\\
+0&0&0&\dots&\lambda
+\end{pmatrix}
+\]
+$\Rightarrow J_\lambda -\lambda I$ ist nilpotent
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
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