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author | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
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committer | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
commit | 14033ca595b5c933caea3b214d2246529e6845b8 (patch) | |
tree | 0d6d2b2eb34e5ef5df3c517be5c1c9d803fa066c /vorlesungen/slides/9/pf/dreieck.tex | |
parent | Update teil1.tex (diff) | |
parent | Only include buch.ind if it exists. (diff) | |
download | SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.tar.gz SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.zip |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/slides/9/pf/dreieck.tex')
-rw-r--r-- | vorlesungen/slides/9/pf/dreieck.tex | 44 |
1 files changed, 44 insertions, 0 deletions
diff --git a/vorlesungen/slides/9/pf/dreieck.tex b/vorlesungen/slides/9/pf/dreieck.tex new file mode 100644 index 0000000..0a572f3 --- /dev/null +++ b/vorlesungen/slides/9/pf/dreieck.tex @@ -0,0 +1,44 @@ +% +% dreieck.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Verallgemeinerte Dreiecksungleichung} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.32\textwidth} +\begin{block}{Satz} +\[ +|u+v|\le |u|+|v| +\] +Gleichheit wenn lin.~abh. +\end{block} +\begin{block}{Satz} +\[ +\biggl|\sum_i u_i\biggr| +\le +\sum_i |u_i| +\] +Gleichheit wenn $u_i = \lambda_i u$ +\end{block} +\begin{block}{Satz} +\[ +\biggl|\sum_i z_i\biggr| +\le +\sum_i |z_i| +\] +Gleichheit, wenn $z_i=|z_i|c$, $c\in\mathbb{C}$ +\end{block} +\end{column} +\begin{column}{0.68\textwidth} +\begin{center} +\includegraphics[width=\textwidth]{../../buch/chapters/80-wahrscheinlichkeit/images/dreieck.pdf} +\end{center} +\end{column} +\end{columns} +\end{frame} +\egroup |