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| author | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-13 17:01:22 +0100 |
|---|---|---|
| committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-13 17:01:22 +0100 |
| commit | da620556baa588139e2abb7fda1e223b0c793f42 (patch) | |
| tree | 64eeeb1815972f97f83ddf7a872ea66138b52d20 /buch/chapters/10-vektorenmatrizen | |
| parent | rref stuff (diff) | |
| download | SeminarMatrizen-da620556baa588139e2abb7fda1e223b0c793f42.tar.gz SeminarMatrizen-da620556baa588139e2abb7fda1e223b0c793f42.zip | |
geometry
Diffstat (limited to 'buch/chapters/10-vektorenmatrizen')
| -rw-r--r-- | buch/chapters/10-vektorenmatrizen/images/strukturen.pdf | bin | 45336 -> 45339 bytes | |||
| -rw-r--r-- | buch/chapters/10-vektorenmatrizen/images/strukturen.tex | 8 | ||||
| -rw-r--r-- | buch/chapters/10-vektorenmatrizen/linear.tex | 11 |
3 files changed, 10 insertions, 9 deletions
diff --git a/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf b/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf Binary files differindex c2d545e..14f7e59 100644 --- a/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf +++ b/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf diff --git a/buch/chapters/10-vektorenmatrizen/images/strukturen.tex b/buch/chapters/10-vektorenmatrizen/images/strukturen.tex index 0006699..02ca71d 100644 --- a/buch/chapters/10-vektorenmatrizen/images/strukturen.tex +++ b/buch/chapters/10-vektorenmatrizen/images/strukturen.tex @@ -52,7 +52,7 @@ \end{scope} \fill[rounded corners=0.5cm,color=white] (-2,-10.5) rectangle (6,-0.5); -\fill[rounded corners=0.5cm,color=blue!20] (-6,-10.0) rectangle (2,0); +\fill[rounded corners=0.5cm,color=blue!20] (-6,-10.1) rectangle (2,0); %\draw[rounded corners=0.5cm] (-6,-10.0) rectangle (2,0); % Vektorraum @@ -94,7 +94,7 @@ \draw[rounded corners=0.3cm] (-1.8,-10.3) rectangle (5.8,-4.5); % boundary of blue area -\draw[rounded corners=0.5cm] (-6,-10.0) rectangle (2,0); +\draw[rounded corners=0.5cm] (-6,-10.1) rectangle (2,0); \begin{scope}[yshift=-5cm] \node at (5.6,0) [left] {{\bf Ring mit Eins}:}; @@ -108,8 +108,8 @@ \end{scope} \fill[rounded corners=0.1cm,color=darkgreen!20] - (-1.6,-9.8) rectangle (1.6,-6.9); -\draw[rounded corners=0.1cm] (-1.6,-9.8) rectangle (1.6,-6.9); + (-1.6,-9.9) rectangle (1.6,-6.9); +\draw[rounded corners=0.1cm] (-1.6,-9.9) rectangle (1.6,-6.9); \begin{scope}[yshift=-7cm] \node at (0,-0.3) {{\bf Körper}:\strut}; diff --git a/buch/chapters/10-vektorenmatrizen/linear.tex b/buch/chapters/10-vektorenmatrizen/linear.tex index 1311ded..cdd1693 100644 --- a/buch/chapters/10-vektorenmatrizen/linear.tex +++ b/buch/chapters/10-vektorenmatrizen/linear.tex @@ -687,7 +687,7 @@ Für ein Gleichungssystem $Ax=b$ mit Schlusstableau 0& 0&\dots & 0& 0& 0&\dots & 1&c_{i_2,j_2} &\dots &c_{i_2j_k} &d_{i_2} \\ 0& 0&\dots & 0& 0& 0&\dots & 0& 0&\dots &c_{i_2+1,j_k}&d_{i_2+1}\\[-2pt] \vdots&\vdots&\ddots&\vdots &\vdots &\vdots&\ddots&\vdots&\vdots &\ddots&\vdots &\vdots \\ - 0& 0&\dots & 0& 0& 0&\dots & 0& 0&\dots &c_{mj_k} &d_{m} \\ + 0& 0&\dots & 0& 0& 0&\dots & 0& 0&\dots & 0&d_{m} \\ \hline \end{tabular} \end{equation} @@ -717,7 +717,7 @@ d_{m} -c_{2j_1}\\ \vdots\\ -c_{i_1,j_1}\\ -1\\ +{\color{darkgreen}1}\\ \vdots\\ 0\\ 0\\ @@ -734,7 +734,7 @@ d_{m} -c_{j_1+1,j_2}\\ \vdots\\ -c_{i_2,j_2}\\ -1\\ +{\color{darkgreen}1}\\ \vdots\\ 0\\ \end{pmatrix} @@ -752,7 +752,7 @@ d_{m} -c_{i_2,j_k}\\ -c_{i_2+1,j_k}\\ \vdots\\ --c_{m,j_k}\\ +0\\ \end{pmatrix} \; \right| @@ -837,6 +837,7 @@ Seite~\pageref{buch:vektorenmatrizen:satz:gruppenregeln} die Eigenschaft $A^{-1}A=I$ ganz allgemein gezeigt. \subsubsection{Determinante} +XXX TODO % % Lineare Abbildungen @@ -1131,4 +1132,4 @@ n-\operatorname{def}A. \end{satz} \subsubsection{Quotient} -TODO +TODO: $\operatorname{im} A \simeq \Bbbk^m/\ker A$ |