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author | Andreas Müller <andreas.mueller@othello.ch> | 2021-02-16 22:05:38 +0100 |
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committer | Andreas Müller <andreas.mueller@othello.ch> | 2021-02-16 22:05:38 +0100 |
commit | 69c5a77e6f008330327f2697f9c77cea6f2e1c3a (patch) | |
tree | 83d7adac3f35346ae363e11128d5699bbe466c3b /vorlesungen/slides/1/vektorraum.tex | |
parent | start making slides (diff) | |
download | SeminarMatrizen-69c5a77e6f008330327f2697f9c77cea6f2e1c3a.tar.gz SeminarMatrizen-69c5a77e6f008330327f2697f9c77cea6f2e1c3a.zip |
chapter 1 slides
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-rw-r--r-- | vorlesungen/slides/1/vektorraum.tex | 54 |
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diff --git a/vorlesungen/slides/1/vektorraum.tex b/vorlesungen/slides/1/vektorraum.tex new file mode 100644 index 0000000..2566085 --- /dev/null +++ b/vorlesungen/slides/1/vektorraum.tex @@ -0,0 +1,54 @@ +% +% vektorraum.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\begin{frame}[t] +\frametitle{Vektorraum} +\vspace{-10pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Operationen} +Addition: +\[ +\begin{pmatrix}a_1\\\vdots\\a_n \end{pmatrix} ++ +\begin{pmatrix}b_1\\\vdots\\b_n \end{pmatrix} += +\begin{pmatrix}a_1+b_1\\\vdots\\a_n+b_n \end{pmatrix} +\] +Skalarmultiplikation: +\[ +\lambda\begin{pmatrix}a_1\\\vdots\\a_n \end{pmatrix} += +\begin{pmatrix}\lambda a_1\\\vdots\\\lambda a_n \end{pmatrix} +\] +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<2->{% +\begin{block}{Additive Gruppe} +$\mathbb{R}^n$ ist eine Gruppe bezüglich der Addition +mit +\[ +0=\begin{pmatrix}0\\\vdots\\0\end{pmatrix}, +\qquad +-a += +-\begin{pmatrix}a_1\\\vdots\\a_n\end{pmatrix} += +\begin{pmatrix}-a_1\\\vdots\\-a_n\end{pmatrix} +\] +\end{block}} +\vspace{-5pt} +\uncover<3->{% +\begin{block}{Skalarmultiplikation} +Distributivgesetz +\begin{align*} +(\lambda+\mu)a&=\lambda a + \mu a\\ +\lambda (a+b)&=\lambda a + \lambda b +\end{align*} +\end{block}} +\end{column} +\end{columns} +\end{frame} |