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Diffstat (limited to 'vorlesungen/slides/3/einsetzen.tex')
| -rw-r--r-- | vorlesungen/slides/3/einsetzen.tex | 30 |
1 files changed, 17 insertions, 13 deletions
diff --git a/vorlesungen/slides/3/einsetzen.tex b/vorlesungen/slides/3/einsetzen.tex index 936100d..7f54abb 100644 --- a/vorlesungen/slides/3/einsetzen.tex +++ b/vorlesungen/slides/3/einsetzen.tex @@ -9,41 +9,45 @@ \[ \begin{array}{rcrcrcrcrcrcr} p(X)&=&a_nX^n&+&a_{n-1}X^{n-1}&+&\dots&+&a_2X^2&+&a_1X&+&a_0\phantom{I}\\ -\bigg\downarrow\hspace*{4pt} & & -\bigg\downarrow\hspace*{4pt} & & -\bigg\downarrow\hspace*{10pt} & & & & -\bigg\downarrow\hspace*{4pt} & & -\bigg\downarrow\hspace*{2pt} & & -\bigg\downarrow\hspace*{0pt} \\ -p(A)&=&a_nA^n&+&a_{n-1}A^{n-1}&+&\dots&+&a_2A^2&+&a_1A&+&a_0 I +\uncover<2->{\bigg\downarrow\hspace*{4pt}} & & +\uncover<3->{\bigg\downarrow\hspace*{4pt}} & & +\uncover<4->{\bigg\downarrow\hspace*{10pt}} & & & & +\uncover<5->{\bigg\downarrow\hspace*{4pt}} & & +\uncover<6->{\bigg\downarrow\hspace*{2pt}} & & +\uncover<7->{\bigg\downarrow\hspace*{0pt}} \\ +\uncover<2->{p(A)}&\uncover<3->{=&a_nA^n}&\uncover<4->{+&a_{n-1}A^{n-1}}&\uncover<5->{+&\dots&+&a_2A^2}&\uncover<6->{+&a_1A}&\uncover<7->{+&a_0 I} \end{array} \] \vspace{-10pt} \begin{columns}[t,onlytextwidth] \begin{column}{0.48\textwidth} +\uncover<8->{% \begin{block}{Nilpotente Matrizen} $p(X) = (X-a)^n$ \[ -p(A) = 0 +\uncover<9->{p(A) = 0} +\uncover<10->{ \quad\Rightarrow\quad -\text{$A$ ist nilpotent} +\text{$A-aI$ ist nilpotent}} \] -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<11->{% \begin{block}{Eigenwerte} $p(X) = (X-\lambda_1)(X-\lambda_2)$,\\ $A$ eine $2\times 2$-Matrix \[ -p(A)=0\quad\Rightarrow\quad +\uncover<12->{p(A)=0} +\uncover<13->{\quad\Rightarrow\quad \left\{ \begin{aligned} &\text{$A-\lambda_1I$ ist singulär}\\ &\text{$A-\lambda_2I$ ist singulär} \end{aligned} -\right. +\right.} \] -\end{block} +\end{block}} \end{column} \end{columns} |