diff options
Diffstat (limited to 'vorlesungen/slides/3')
| -rw-r--r-- | vorlesungen/slides/3/Makefile.inc | 10 | ||||
| -rw-r--r-- | vorlesungen/slides/3/chapter.tex | 7 | ||||
| -rw-r--r-- | vorlesungen/slides/3/motivation.tex | 106 | ||||
| -rw-r--r-- | vorlesungen/slides/3/polynome.tex | 9 |
4 files changed, 132 insertions, 0 deletions
diff --git a/vorlesungen/slides/3/Makefile.inc b/vorlesungen/slides/3/Makefile.inc new file mode 100644 index 0000000..a58ee05 --- /dev/null +++ b/vorlesungen/slides/3/Makefile.inc @@ -0,0 +1,10 @@ + +# +# Makefile.inc -- additional depencencies +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapter3 = \ + ../slides/3/motivation.tex \ + ../slides/3/chapter.tex + diff --git a/vorlesungen/slides/3/chapter.tex b/vorlesungen/slides/3/chapter.tex new file mode 100644 index 0000000..f8d422e --- /dev/null +++ b/vorlesungen/slides/3/chapter.tex @@ -0,0 +1,7 @@ +% +% chapter.tex +% +% (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi +% +\folie{3/polynome.tex} +\folie{3/motivation.tex} diff --git a/vorlesungen/slides/3/motivation.tex b/vorlesungen/slides/3/motivation.tex new file mode 100644 index 0000000..cf28d46 --- /dev/null +++ b/vorlesungen/slides/3/motivation.tex @@ -0,0 +1,106 @@ +% +% motivation.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\begin{frame}[t] +\frametitle{Motivation} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.24\textwidth} +\begin{block}{Imaginäre Einheit} +\vspace{-15pt} +\begin{align*} +J &= \begin{pmatrix} 0&-1\\1&0\end{pmatrix} +\\ +p(X) &= X^2 + 1 +\\ +p(J) &= J^2 + I = 0 +\end{align*} +\end{block} +\end{column} +\begin{column}{0.25\textwidth} +\uncover<2->{% +\begin{block}{Wurzel $\sqrt{2}$} +\vspace{-15pt} +\begin{align*} +W&=\begin{pmatrix}0&2\\1&0\end{pmatrix} +\\ +p(X) &= X^2-2 +\\ +p(W) &= W^2-2I=0 +\end{align*} +\end{block}} +\end{column} +\begin{column}{0.41\textwidth} +\uncover<3->{% +\begin{block}{Drehmatrix} +\vspace{-15pt} +\begin{align*} +D&=\begin{pmatrix} +\cos \frac{\pi}{1291} & -\sin\frac{\pi}{1291}\\ +\sin \frac{\pi}{1291} & \cos\frac{\pi}{1291} +\end{pmatrix} +\\ +p(X)&= \only<-3>{X^{1291}+1\phantom{+\frac{\mathstrut}{\mathstrut}}} +\only<4->{X^2-2X\cos\frac{\pi\mathstrut}{1291\mathstrut}+I} +\\ +p(D) &= \only<-3>{D^{1291}+I\phantom{+\frac{\mathstrut}{\mathstrut}}} +\only<4->{D^2-2D\cos\frac{\pi\mathstrut}{1291\mathstrut}+I} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\vspace{-20pt} +\uncover<5->{ +\begin{block}{3D-Beispiel} +$p(x) = -x^3-5x^2+5x+1$ +\[ +\only<5-8>{ +A= +\begin{pmatrix*}[r] +-5&-1&1\\ +-5&-2&3\\ +-1&-1&2 +\end{pmatrix*}} +\only<6-8>{ +\quad\Rightarrow\quad} +\uncover<6->{ +- +\only<-9>{A^3}\only<10->{ +\begin{pmatrix*}[r] +-169&-35&35\\ +-185&-39&40\\ + -45&-10&11 +\end{pmatrix*}} +-5 +\only<-8>{A^2}\only<9->{ +\begin{pmatrix*}[r] +29&6&-6\\ +32&6&-5\\ + 8&1& 0 +\end{pmatrix*}} ++5 +\only<-7>{A}\only<8->{ +\begin{pmatrix*}[r] +-5&-1&1\\ +-5&-2&3\\ +-1&-1&2 +\end{pmatrix*}} ++ +\only<-6>{I}\only<7->{ +\begin{pmatrix*}[r] +1&0&0\\ +0&1&0\\ +0&0&1 +\end{pmatrix*}} +} +\uncover<11->{=0} +\] +\end{block}} +\vspace{-10pt} +\uncover<12->{% +{\usebeamercolor[fg]{title}$\Rightarrow$ +Rechenregeln von Matrizen können durch Polynome ausgedrückt werden} +} +\end{frame} diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex new file mode 100644 index 0000000..6ca0009 --- /dev/null +++ b/vorlesungen/slides/3/polynome.tex @@ -0,0 +1,9 @@ +% +% polynome.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\begin{frame} +\frametitle{Polynome} + +\end{frame} |