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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-04-11 10:30:05 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-04-11 10:30:05 +0200 |
commit | 15881729aa3f1293d546a1692a02094ed3f24e2b (patch) | |
tree | 7a051091d6f507ad3ab28dbd227206ad1288f368 /vorlesungen/slides/7/drehung.tex | |
parent | phasen (diff) | |
download | SeminarMatrizen-15881729aa3f1293d546a1692a02094ed3f24e2b.tar.gz SeminarMatrizen-15881729aa3f1293d546a1692a02094ed3f24e2b.zip |
phases
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/7/drehung.tex | 53 |
1 files changed, 36 insertions, 17 deletions
diff --git a/vorlesungen/slides/7/drehung.tex b/vorlesungen/slides/7/drehung.tex index ae0dbe3..7744e99 100644 --- a/vorlesungen/slides/7/drehung.tex +++ b/vorlesungen/slides/7/drehung.tex @@ -13,12 +13,20 @@ \begin{columns}[t,onlytextwidth] \begin{column}{0.38\textwidth} \begin{block}{Drehung} +{\color{blue}Längen}, {\color<2->{blue}Winkel}, +{\color<2->{darkgreen}Orientierung} +erhalten +\uncover<2->{ \[ \operatorname{SO}(2) = -\operatorname{SL}_2(\mathbb{R}) \cap \operatorname{O}(2) -\] +{\color{blue}\operatorname{O}(2)} +\cap +{\color{darkgreen}\operatorname{SL}_2(\mathbb{R})} +\]} +\vspace{-20pt} \end{block} +\uncover<3->{% \begin{block}{Zusammensetzung} Eine Drehung muss als Zusammensetzung geschrieben werden können: \[ @@ -31,7 +39,9 @@ D_{\alpha} = DST \] -\end{block} +\end{block}} +\vspace{-10pt} +\uncover<12->{% \begin{block}{Beispiel} \vspace{-12pt} \[ @@ -43,9 +53,10 @@ D_{60^\circ} \begin{pmatrix}1&0\\\frac{\sqrt{3}}2&1\end{pmatrix} } \] -\end{block} +\end{block}} \end{column} \begin{column}{0.58\textwidth} +\uncover<4->{% \begin{block}{Ansatz} \vspace{-12pt} \begin{align*} @@ -64,7 +75,7 @@ c^{-1}&0\\ t&1 \end{pmatrix} \\ -&= +&\uncover<5->{= \begin{pmatrix} c^{-1}&0\\ 0 &c @@ -73,40 +84,48 @@ c^{-1}&0\\ -st&-s\\ t& 1 \end{pmatrix} +} \\ -&= +&\uncover<6->{= \begin{pmatrix} --stc^{-1}&{\color{darkgreen}sc^{-1}}\\ -{\color{blue}ct}&{\color{red}c} -\end{pmatrix} -= +{\color<11->{orange}-stc^{-1}}&{\color<10->{darkgreen}sc^{-1}}\\ +{\color<9->{blue}ct}&{\color<8->{red}c} +\end{pmatrix}} +\uncover<7->{= \begin{pmatrix} -\cos\alpha & {\color{darkgreen}- \sin\alpha} \\ -{\color{blue}\sin\alpha} & \phantom{-} {\color{red}\cos\alpha} -\end{pmatrix} +{\color<11->{orange}\cos\alpha} & {\color<10->{darkgreen}- \sin\alpha} \\ +{\color<9->{blue}\sin\alpha} & \phantom{-} {\color<8->{red}\cos\alpha} +\end{pmatrix}} \end{align*} -\end{block} +\end{block}} \vspace{-10pt} +\uncover<7->{% \begin{block}{Koeffizientenvergleich} \vspace{-15pt} \begin{align*} +\uncover<8->{ {\color{red} c} &= -{\color{red}\cos\alpha } +{\color{red}\cos\alpha }} && & +\uncover<9->{ {\color{blue} -t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$} \\ +t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$}}\\ +\uncover<10->{ {\color{darkgreen}sc^{-1}}&={\color{darkgreen}-\sin\alpha} & &\Rightarrow& {\color{darkgreen}s}&={\color{darkgreen}-\sin\alpha}\cos\alpha +} \\ +\uncover<11->{ {\color{orange} -stc^{-t}} &= \rlap{$\sin\alpha\tan\alpha = \cos\alpha \quad $} +} \end{align*} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} |