diff options
Diffstat (limited to 'vorlesungen/slides/5/kernbild.tex')
| -rw-r--r-- | vorlesungen/slides/5/kernbild.tex | 28 |
1 files changed, 23 insertions, 5 deletions
diff --git a/vorlesungen/slides/5/kernbild.tex b/vorlesungen/slides/5/kernbild.tex index f0bd6fa..3890717 100644 --- a/vorlesungen/slides/5/kernbild.tex +++ b/vorlesungen/slides/5/kernbild.tex @@ -10,29 +10,38 @@ \vspace{-15pt} \begin{columns}[t,onlytextwidth] \begin{column}{0.48\textwidth} +\uncover<1->{% \begin{block}{Kern} Lineare Abbildung $f\colon V\to V$ \[ \ker f = \mathcal{K}(F) = \{v\in V\;|\; f(v)=0\} \] -\end{block} +\end{block}} +\uncover<3->{% \begin{block}{Kern von $A^k$} \[ \mathcal{K}^k(f) = \operatorname{ker} f^k \] \begin{align*} +\uncover<5->{ \mathcal{K}^k(f) &= \{v\in V\;|\; f^{k}(v)=0\} +} \\ +\uncover<6->{ &\subset \{v\in V\;|\; f^{k+1}(v)=0\} +} \\ +\uncover<7->{ &=\mathcal{K}^{k+1}(f) +} \end{align*} -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<2->{% \begin{block}{Bild} Lineare Abbildung $f\colon V\to V$ \[ @@ -42,27 +51,36 @@ Lineare Abbildung $f\colon V\to V$ = \{f(v)\;|\; v\in V\} \] -\end{block} +\end{block}} +\uncover<4->{% \begin{block}{Bild von $A^k$} \[ \mathcal{J}^k(f) = \operatorname{im}f^k \] \begin{align*} +\uncover<8->{ \mathcal{J}^k(f) &= \operatorname{im}f^k = \operatorname{im}(f^{k}\circ f) +} \\ +\uncover<9->{ &= \{f^{k-1} w\;|\; w = f(v)\} +} \\ +\uncover<10->{ &\subset \{f^{k-1} w\;|\; w \in V\} +} \\ -&\mathcal{J}^{k-1}(f) +\uncover<11->{ +&=\mathcal{J}^{k-1}(f) +} \end{align*} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} |