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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-05-27 16:21:20 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-05-27 16:21:20 +0200 |
commit | 033606388c772b07adcb0f7f5619862674068fad (patch) | |
tree | 561622986c2ec80575dae265d509916c8418f299 /vorlesungen/slides/8/wavelets/matrixdilatation.tex | |
parent | Fourier-Transformation (diff) | |
download | SeminarMatrizen-033606388c772b07adcb0f7f5619862674068fad.tar.gz SeminarMatrizen-033606388c772b07adcb0f7f5619862674068fad.zip |
add new slides
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-rw-r--r-- | vorlesungen/slides/8/wavelets/matrixdilatation.tex | 39 |
1 files changed, 39 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/wavelets/matrixdilatation.tex b/vorlesungen/slides/8/wavelets/matrixdilatation.tex new file mode 100644 index 0000000..3536736 --- /dev/null +++ b/vorlesungen/slides/8/wavelets/matrixdilatation.tex @@ -0,0 +1,39 @@ +% +% matrixdilatation.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Dilatation in Matrixform} +Dilatationsfaktor $a$, skaliertes Wavelet beim Knoten $k$ mit Spektrum +$\tilde{D}_{1/a}g$ +\begin{align*} +D_{g,a}e_k +&= +\chi +\begin{pmatrix} +g(a\lambda_1)& 0 & \dots & 0 \\ + 0 &g(a\lambda_2)& \dots & 0 \\ + \vdots & \vdots & \ddots & \vdots \\ + 0 & 0 & \dots &g(a\lambda_n) +\end{pmatrix} +\chi^t +e_k +\intertext{\uncover<2->{``verschmierter'' Standardbasisvektor am Knoten $k$}} +\uncover<2->{D_he_k +&= +\chi +\begin{pmatrix} +h(\lambda_1)& 0 & \dots & 0 \\ + 0 &h(\lambda_2)& \dots & 0 \\ + \vdots & \vdots & \ddots & \vdots \\ + 0 & 0 & \dots &h(\lambda_n) +\end{pmatrix} +\chi^t +e_k} +\end{align*} +\end{frame} +\egroup |