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authorAndreas Müller <andreas.mueller@ost.ch>2021-02-13 17:01:22 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2021-02-13 17:01:22 +0100
commitda620556baa588139e2abb7fda1e223b0c793f42 (patch)
tree64eeeb1815972f97f83ddf7a872ea66138b52d20 /buch/chapters/10-vektorenmatrizen
parentrref stuff (diff)
downloadSeminarMatrizen-da620556baa588139e2abb7fda1e223b0c793f42.tar.gz
SeminarMatrizen-da620556baa588139e2abb7fda1e223b0c793f42.zip
geometry
Diffstat (limited to 'buch/chapters/10-vektorenmatrizen')
-rw-r--r--buch/chapters/10-vektorenmatrizen/images/strukturen.pdfbin45336 -> 45339 bytes
-rw-r--r--buch/chapters/10-vektorenmatrizen/images/strukturen.tex8
-rw-r--r--buch/chapters/10-vektorenmatrizen/linear.tex11
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
index c2d545e..14f7e59 100644
--- a/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf
+++ b/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf
Binary files differ
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: $\operatorname{im} A \simeq \Bbbk^m/\ker A$