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author | Roy Seitz <roy.seitz@ost.ch> | 2021-02-22 08:48:36 +0100 |
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committer | Roy Seitz <roy.seitz@ost.ch> | 2021-02-22 08:48:36 +0100 |
commit | a82da67587b049e54dcd53e76b4220d22a60d842 (patch) | |
tree | 8b0717987839cf0e6cac6c4297f95f94f695f247 /vorlesungen/slides/1/dreieck.tex | |
parent | Typos. (diff) | |
parent | add ende (diff) | |
download | SeminarMatrizen-a82da67587b049e54dcd53e76b4220d22a60d842.tar.gz SeminarMatrizen-a82da67587b049e54dcd53e76b4220d22a60d842.zip |
Merge remote-tracking branch 'origin/master'
Diffstat (limited to 'vorlesungen/slides/1/dreieck.tex')
-rw-r--r-- | vorlesungen/slides/1/dreieck.tex | 62 |
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diff --git a/vorlesungen/slides/1/dreieck.tex b/vorlesungen/slides/1/dreieck.tex new file mode 100644 index 0000000..f4909e2 --- /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} |