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Diffstat (limited to 'vorlesungen/slides/5/nilpotent.tex')
| -rw-r--r-- | vorlesungen/slides/5/nilpotent.tex | 176 |
1 files changed, 176 insertions, 0 deletions
diff --git a/vorlesungen/slides/5/nilpotent.tex b/vorlesungen/slides/5/nilpotent.tex new file mode 100644 index 0000000..9b7ded1 --- /dev/null +++ b/vorlesungen/slides/5/nilpotent.tex @@ -0,0 +1,176 @@ +% +% nilpotent.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\def\feld#1{ + \fill[color=red!20] (#1,0) rectangle ({#1+1},12); +} +\begin{frame}[t] +\frametitle{$\mathcal{J}^k(f)$ und $\mathcal{K}^k(f)$ für nilpotente Matrizen} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.42\textwidth} +Matrix mit dem dargestellten Verlauf von +${\color{red}\dim\mathcal{K}^k(A)}$ +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=0.42] + +\only<2->{ + \feld{0} + \feld{1} + \feld{2} + \feld{3} +} +\only<2->{ \feld{4} } +\only<3->{ \feld{5} } +\only<2->{ \feld{6} } +\only<3->{ \feld{7} } +\only<4->{ \feld{8} } +\only<5->{ \feld{9} } +\only<6->{ \feld{10} } +\only<7->{ \feld{11} } + +\only<1>{ \node at (6,0) [below] {$k=0$}; } +\only<2>{ \node at (6,0) [below] {$k=1$}; } +\only<3>{ \node at (6,0) [below] {$k=2$}; } +\only<4>{ \node at (6,0) [below] {$k=3$}; } +\only<5>{ \node at (6,0) [below] {$k=4$}; } +\only<6>{ \node at (6,0) [below] {$k=5$}; } +\only<7>{ \node at (6,0) [below] {$k=6$}; } + +\draw (0,0) rectangle (12,12); +\only<1>{ + \foreach \x in {1,...,12}{ + \node at ({\x-0.5},{12-\x+0.5}) {$1$}; + } +} +\only<2->{ + \foreach \x in {1,...,12}{ + \node at ({\x-0.5},{12-\x+0.5}) {$0$}; + } +} +\only<2>{ + \foreach \x in {7,...,11}{ + \node at ({\x+0.5},{12-\x+0.5}) {$1$}; + } +} +\only<3->{ + \foreach \x in {7,...,11}{ + \node at ({\x+0.5},{12-\x+0.5}) {$0$}; + } +} +\only<3>{ + \foreach \x in {8,...,11}{ + \node at ({\x+0.5},{13-\x+0.5}) {$1$}; + } +} +\only<4->{ + \foreach \x in {8,...,11}{ + \node at ({\x+0.5},{13-\x+0.5}) {$0$}; + } +} +\only<4>{ + \foreach \x in {9,...,11}{ + \node at ({\x+0.5},{14-\x+0.5}) {$1$}; + } +} +\only<5->{ + \foreach \x in {9,...,11}{ + \node at ({\x+0.5},{14-\x+0.5}) {$0$}; + } +} +\only<5>{ + \foreach \x in {10,...,11}{ + \node at ({\x+0.5},{15-\x+0.5}) {$1$}; + } +} +\only<6->{ + \foreach \x in {10,...,11}{ + \node at ({\x+0.5},{15-\x+0.5}) {$0$}; + } +} +\only<6>{ + \foreach \x in {11,...,11}{ + \node at ({\x+0.5},{16-\x+0.5}) {$1$}; + } +} +\only<7->{ + \foreach \x in {11,...,11}{ + \node at ({\x+0.5},{16-\x+0.5}) {$0$}; + } +} +\draw[line width=0.1pt] + (0,11) -- (2,11) -- (2,9) -- (4,9) -- (4,6) -- (12,6); +\draw[line width=0.1pt] + (1,12) -- (1,10) -- (3,10) -- (3,8) -- (6,8) -- (6,0); +\only<2>{ + \node at (5.5,7.5) {$1$}; +} +\only<3->{ + \node at (5.5,7.5) {$0$}; +} +\end{tikzpicture} +\end{center} +\end{column} +\begin{column}{0.56\textwidth} +\vspace{-15pt} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\pfad{ + (0,0) -- (1,3) -- (2,4) -- (3,4.5) -- (4,5) -- (5,5.5) -- (6,6) +} +\fill[color=orange!20] \pfad -- (0,6) -- cycle; +\fill[color=darkgreen!20] \pfad -- (6,0) -- cycle; +\foreach \y in {0.5,1,...,5.75}{ + \draw[line width=0.1pt] (0,\y) -- (6,\y); +} +\draw[line width=1.4pt] \pfad; +\draw[->] (-0.1,6) -- (6.5,6); \node at (-0.1,6) [left] {$n$}; +\draw[->] (-0.1,0) -- (6.5,0); \node at (-0.1,0) [left] {$0$}; +\fill (0,0) circle[radius=0.05]; +\fill (1,3) circle[radius=0.05]; +\fill (2,4) circle[radius=0.05]; +\fill (3,4.5) circle[radius=0.05]; +\fill (4,5) circle[radius=0.05]; +\fill (5,5.5) circle[radius=0.05]; +\fill (6,6) circle[radius=0.05]; +\only<1>{ + \fill[color=red] (0,0) circle[radius=0.08]; +} +\only<2>{ + \fill[color=red] (1,3) circle[radius=0.08]; + \draw[color=red] (0,3) -- (1,3); + \node[color=red] at (0,3) [left] {$6$}; +} +\only<3>{ + \fill[color=red] (2,4) circle[radius=0.08]; + \draw[color=red] (0,4) -- (2,4); + \node[color=red] at (0,4) [left] {$8$}; +} +\only<4>{ + \fill[color=red] (3,4.5) circle[radius=0.08]; + \draw[color=red] (0,4.5) -- (3,4.5); + \node[color=red] at (0,4.5) [left] {$9$}; +} +\only<5>{ + \fill[color=red] (4,5.0) circle[radius=0.08]; + \draw[color=red] (0,5.0) -- (4,5.0); + \node[color=red] at (0,5.0) [left] {$10$}; +} +\only<6>{ + \fill[color=red] (5,5.5) circle[radius=0.08]; + \draw[color=red] (0,5.5) -- (5,5.5); + \node[color=red] at (0,5.5) [left] {$11$}; +} +\only<7>{ + \fill[color=red] (6,6.0) circle[radius=0.08]; +} +\draw[color=white] (-0.7,0) -- (-0.7,6); +\end{tikzpicture} +\end{center} +\end{column} +\end{columns} +\end{frame} +\egroup |