3 files changed, 102 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/Makefile.inc b/vorlesungen/slides/8/Makefile.inc
index cc2c497..233835a 100644
--- a/vorlesungen/slides/8/Makefile.inc
+++ b/vorlesungen/slides/8/Makefile.inc
@@ -12,6 +12,7 @@ chapter8 =								\
 	../slides/8/inzidenzd.tex					\
 	../slides/8/diffusion.tex					\
 	../slides/8/laplace.tex						\
+	../slides/8/produkt.tex						\
 	../slides/8/fourier.tex						\
 	../slides/8/spanningtree.tex					\
 	../slides/8/pfade/adjazenz.tex					\
diff --git a/vorlesungen/slides/8/chapter.tex b/vorlesungen/slides/8/chapter.tex
index b29145f..ac06775 100644
--- a/vorlesungen/slides/8/chapter.tex
+++ b/vorlesungen/slides/8/chapter.tex
@@ -10,6 +10,7 @@
 \folie{8/inzidenzd.tex}
 \folie{8/diffusion.tex}
 \folie{8/laplace.tex}
+\folie{8/produkt.tex}
 \folie{8/fourier.tex}
 \folie{8/spanningtree.tex}
 
diff --git a/vorlesungen/slides/8/produkt.tex b/vorlesungen/slides/8/produkt.tex
new file mode 100644
index 0000000..1d8b725
--- /dev/null
+++ b/vorlesungen/slides/8/produkt.tex
@@ -0,0 +1,100 @@
+%
+% produkt.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Inzidenz- und Laplace-Matrix}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.40\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\r{2.2}
+
+\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)});
+\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)});
+\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)});
+\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)});
+\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)});
+
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C);
+\draw[color=white,line width=5pt] (B) -- (D);
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D);
+
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B);
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C);
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D);
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E);
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A);
+
+\draw (A) circle[radius=0.2];
+\draw (B) circle[radius=0.2];
+\draw (C) circle[radius=0.2];
+\draw (D) circle[radius=0.2];
+\draw (E) circle[radius=0.2];
+
+\node at (A) {$1$};
+\node at (B) {$2$};
+\node at (C) {$3$};
+\node at (D) {$4$};
+\node at (E) {$5$};
+\node at (0,0) {$G$};
+
+\node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) [above right] {$\scriptstyle 1$};
+\node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) [above left] {$\scriptstyle 2$};
+\node at ($0.5*(C)+0.5*(D)+(0.05,0)$) [left] {$\scriptstyle 3$};
+\node at ($0.5*(D)+0.5*(E)$) [below] {$\scriptstyle 4$};
+\node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) [below right] {$\scriptstyle 5$};
+\node at ($0.6*(A)+0.4*(C)$) [above] {$\scriptstyle 6$};
+\node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 7$};
+
+\end{tikzpicture}
+\end{center}
+\vspace{-15pt}
+\begin{block}{Berechne}
+\vspace{-20pt}
+\begin{align*}
+\uncover<4->{L(G)}&\uncover<4->{=}B(G)B(G)^t
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.58\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\dx{0.84}
+\def\dy{0.48}
+
+\node at (0,0) {$\displaystyle
+\begin{aligned}
+B(G)
+&=
+\begin{pmatrix*}[r]
+-1& 0& 0& 0&+1&-1& 0\\
++1&-1& 0& 0& 0& 0&-1\\
+ 0&+1&-1& 0& 0&+1& 0\\
+ 0& 0&+1&-1& 0& 0&+1\\
+ 0& 0& 0&+1&-1& 0& 0
+\end{pmatrix*}
+\\[20pt]
+\uncover<2->{
+L(G)
+&=
+\begin{pmatrix*}[r]
+ 3&\uncover<3->{-1}&\uncover<3->{-1}&\uncover<3->{ 0}&\uncover<3->{-1}\\
+\uncover<3->{-1}& 3&\uncover<3->{-1}&\uncover<3->{-1}&\uncover<3->{ 0}\\
+\uncover<3->{-1}&\uncover<3->{-1}& 3&\uncover<3->{-1}&\uncover<3->{ 0}\\
+\uncover<3->{ 0}&\uncover<3->{-1}&\uncover<3->{-1}& 3&\uncover<3->{-1}\\
+\uncover<3->{-1}&\uncover<3->{ 0}&\uncover<3->{ 0}&\uncover<3->{-1}& 2
+\end{pmatrix*}}
+\end{aligned}$};
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup