From da620556baa588139e2abb7fda1e223b0c793f42 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 13 Feb 2021 17:01:22 +0100
Subject: geometry

---
 .../10-vektorenmatrizen/images/strukturen.pdf       | Bin 45336 -> 45339 bytes
 .../10-vektorenmatrizen/images/strukturen.tex       |   8 ++++----
 buch/chapters/10-vektorenmatrizen/linear.tex        |  11 ++++++-----
 3 files changed, 10 insertions(+), 9 deletions(-)

(limited to 'buch/chapters')

diff --git a/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf b/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf
index c2d545e..14f7e59 100644
Binary files a/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf and b/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf 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: $\operatorname{im} A \simeq \Bbbk^m/\ker A$
-- 
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