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authorAndreas Müller <andreas.mueller@ost.ch>2021-05-27 16:21:20 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-05-27 16:21:20 +0200
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parentFourier-Transformation (diff)
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+%
+% 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