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authorAndreas Müller <andreas.mueller@ost.ch>2021-03-01 08:18:59 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2021-03-01 08:18:59 +0100
commit67addea9bf154558ca3bbc14703c2b0fef8fc60c (patch)
tree035a99ac3914cd68e2db68712565347359fc111d /vorlesungen
parentadd new slides (diff)
downloadSeminarMatrizen-67addea9bf154558ca3bbc14703c2b0fef8fc60c.tar.gz
SeminarMatrizen-67addea9bf154558ca3bbc14703c2b0fef8fc60c.zip
phases, typos
Diffstat (limited to '')
-rw-r--r--vorlesungen/slides/3/Makefile.inc1
-rw-r--r--vorlesungen/slides/3/chapter.tex2
-rw-r--r--vorlesungen/slides/3/division.tex19
-rw-r--r--vorlesungen/slides/3/division2.tex18
-rw-r--r--vorlesungen/slides/3/operatoren.tex2
-rw-r--r--vorlesungen/slides/3/polynome.tex6
-rw-r--r--vorlesungen/slides/test.tex25
7 files changed, 41 insertions, 32 deletions
diff --git a/vorlesungen/slides/3/Makefile.inc b/vorlesungen/slides/3/Makefile.inc
index ac2c3a5..3a55274 100644
--- a/vorlesungen/slides/3/Makefile.inc
+++ b/vorlesungen/slides/3/Makefile.inc
@@ -6,6 +6,7 @@
#
chapter3 = \
../slides/3/motivation.tex \
+ ../slides/3/inverse.tex \
../slides/3/polynome.tex \
../slides/3/division.tex \
../slides/3/division2.tex \
diff --git a/vorlesungen/slides/3/chapter.tex b/vorlesungen/slides/3/chapter.tex
index 672b05a..e63002c 100644
--- a/vorlesungen/slides/3/chapter.tex
+++ b/vorlesungen/slides/3/chapter.tex
@@ -4,6 +4,7 @@
% (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi
%
\folie{3/motivation.tex}
+\folie{3/inverse.tex}
\folie{3/polynome.tex}
\folie{3/division.tex}
\folie{3/division2.tex}
@@ -15,6 +16,7 @@
\folie{3/maximalergrad.tex}
\folie{3/minimalbeispiel.tex}
\folie{3/minimalpolynom.tex}
+\folie{3/drehmatrix.tex}
\folie{3/drehfaktorisierung.tex}
\folie{3/operatoren.tex}
\folie{3/adjunktion.tex}
diff --git a/vorlesungen/slides/3/division.tex b/vorlesungen/slides/3/division.tex
index 0932f48..94df27b 100644
--- a/vorlesungen/slides/3/division.tex
+++ b/vorlesungen/slides/3/division.tex
@@ -11,19 +11,22 @@ $a= X^4- X^3-7X^2+ X+6\in\mathbb{Z}[X]$
und
$b= X^2+X+1\in\mathbb{Z}[X]$
\end{block}
+\uncover<2->{%
\begin{block}{Lösung}
\[
\arraycolsep=1.4pt
\begin{array}{rcrcrcrcrcrcrcrcrcrcr}
-X^4&-& X^3&-&7X^2&+& X&+&6&:&X^2&+&X&+&1&=&X^2&-&2X&-&6=q\\
-\llap{$-($}X^4&+& X^3&+& X^2\rlap{$)$}& & & & & & & & & & & & & & & & \\ \cline{1-5}
- &-&2X^3&-&8X^2&+& X& & & & & & & & & & & & & & \\
- &\llap{$-($}-&2X^3&-&2X^2&-&2X\rlap{$)$}& & & & & & & & & & & & & & \\ \cline{2-7}
- & & &-&6X^2&+&3X&+&6& & & & & & & & & & & & \\
- & & &\llap{$-($}-&6X^2&-&6X&-&6\rlap{$)$}& & & & & & & & & & & & \\ \cline{4-9}
- & & & & & &9X&+&12\rlap{$\mathstrut=r$}& & & & & & & & & & & & \\ \cline{7-9}
+\llap{$($}X^4&-& X^3&-&7X^2&+& X&+&6\rlap{$)$}&\;\mathstrut:\mathstrut&(X^2&+&X&+&1)&=&\uncover<3->{X^2}&\uncover<7->{-&2X}&\uncover<11->{-&6}=q\\
+\uncover<4->{\llap{$-($}X^4&+& X^3&+& X^2\rlap{$)$}}& & & & & & & & & & & & & & & & \\
+ &\uncover<5->{-&2X^3&-&8X^2}&\uncover<6->{+& X}& & & & & & & & & & & & & & \\
+ &\uncover<8->{\llap{$-($}-&2X^3&-&2X^2&-&2X\rlap{$)$}}& & & & & & & & & & & & & & \\
+ & & &\uncover<9->{-&6X^2&+&3X}&\uncover<10->{+&6}& & & & & & & & & & & & \\
+ & & &\uncover<12->{\llap{$-($}-&6X^2&-&6X&-&6\rlap{$)$}}& & & & & & & & & & & & \\
+ & & & & & &\uncover<13->{9X&+&12\rlap{$\mathstrut=r$}}& & & & & & & & & & & &
\end{array}
\]
+\uncover<14->{
Funktioniert weil $b$ normiert ist!
-\end{block}
+}
+\end{block}}
\end{frame}
diff --git a/vorlesungen/slides/3/division2.tex b/vorlesungen/slides/3/division2.tex
index 80d6a75..0602598 100644
--- a/vorlesungen/slides/3/division2.tex
+++ b/vorlesungen/slides/3/division2.tex
@@ -12,21 +12,23 @@ $a(X) = X^4-X^3-7X^2+X+6$
und
$b(X) = 2X^2+X+1$
\end{block}
+\uncover<2->{%
\begin{block}{Lösung}
+\vspace{-15pt}
\[
\arraycolsep=1.4pt
\renewcommand{\arraystretch}{1.2}
\begin{array}{rcrcrcrcrcrcrcrcrcrcr}
-X^4&-& X^3&-& 7X^2&+& X&+& 6&:&2X^2&+&X&+&1&=&\frac12X^2&-&\frac34X&-\frac{27}{8} = q\\
-\llap{$-($}X^4&+&\frac12X^3&+& \frac12X^2\rlap{$)$}& & & & & & & & & & & & & & & \\ \cline{1-5}
- &-&\frac32X^3&-&\frac{15}2X^2&+& X& & & & & & & & & & & & & \\
- &\llap{$-($}-&\frac32X^3&-&\frac{ 3}4X^2&-&\frac{ 3}4X\rlap{$)$}& & & & & & & & & & & & & \\\cline{2-7}
- & & &-&\frac{27}4X^2&+&\frac{ 7}4X&+& 6& & & & & & & & & & & \\
- & & &\llap{$-($}-&\frac{27}4X^2&-&\frac{27}8X&-&\frac{27}{8}\rlap{$)$}& & & & & & & & & & & \\\cline{4-9}
- & & & & & &\frac{41}8X&+&\frac{75}{8}\rlap{$\mathstrut=r$}& & & & & & & & & & & \\
+\llap{$($}X^4&-& X^3&-& 7X^2&+& X&+& 6\rlap{$)$}&\mathstrut\;:\mathstrut&(2X^2&+&X&+&1)&=&\uncover<3->{\frac12X^2}&\uncover<7->{-&\frac34X}&\uncover<11->{-\frac{27}{8}} = q\\
+\uncover<4->{\llap{$-($}X^4&+&\frac12X^3&+& \frac12X^2\rlap{$)$}}& & & & & & & & & & & & & & & \\
+ &\uncover<5->{-&\frac32X^3&-&\frac{15}2X^2}&\uncover<6->{+& X}& & & & & & & & & & & & & \\
+ &\uncover<8->{\llap{$-($}-&\frac32X^3&-&\frac{ 3}4X^2&-&\frac{ 3}4X\rlap{$)$}}& & & & & & & & & & & & & \\
+ & & &\uncover<9->{-&\frac{27}4X^2&+&\frac{ 7}4X}&\uncover<10->{+& 6}& & & & & & & & & & & \\
+ & & &\uncover<12->{\llap{$-($}-&\frac{27}4X^2&-&\frac{27}8X&-&\frac{27}{8}\rlap{$)$}}& & & & & & & & & & & \\
+ & & & & & &\uncover<13->{\frac{41}8X&+&\frac{75}{8}\rlap{$\mathstrut=r$}}& & & & & & & & & & & \\
\end{array}
\]
Funktioniert, weil man in $\Bbbk[X]$ immer normieren kann
-\end{block}
+\end{block}}
\end{frame}
diff --git a/vorlesungen/slides/3/operatoren.tex b/vorlesungen/slides/3/operatoren.tex
index 20b7f3a..161c330 100644
--- a/vorlesungen/slides/3/operatoren.tex
+++ b/vorlesungen/slides/3/operatoren.tex
@@ -13,7 +13,7 @@ $a(X)=a_0+a_1X+\dots+a_nX^n$
a(X)
=
\begin{pmatrix}
-a_0\\a_1\\a_2\\a_3\\\vdots\\a_nX^n
+a_0\\a_1\\a_2\\a_3\\\vdots\\a_n
\end{pmatrix}
\]
\end{block}
diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
index 161a4ed..d7179a0 100644
--- a/vorlesungen/slides/3/polynome.tex
+++ b/vorlesungen/slides/3/polynome.tex
@@ -20,9 +20,9 @@ a(X) = a_nX^n+a_{n-1}X^{n-1} + \dots a_2X^2+a_1X + a_0, a_k\in R
\end{definition}
\begin{itemize}
-\item {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
-\item $\deg 0 = -\infty$
-\item {\em normiertes Polynom}: $a_n=1$
+\item<2-> {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
+\item<3-> $\deg 0 = -\infty$
+\item<4-> {\em normiertes Polynom}: $a_n=1$
\end{itemize}
diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex
index 24d9ffa..3c0348f 100644
--- a/vorlesungen/slides/test.tex
+++ b/vorlesungen/slides/test.tex
@@ -4,18 +4,19 @@
% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil
%
-%\folie{3/motivation.tex}
-%\folie{3/polynome.tex}
-%\folie{3/division.tex}
-%\folie{3/division2.tex}
-%\folie{3/ringstruktur.tex}
-%\folie{3/teilbarkeit.tex}
-%\folie{3/faktorisierung.tex}
-%\folie{3/faktorzerlegung.tex}
-%\folie{3/einsetzen.tex}
-%\folie{3/maximalergrad.tex}
-%\folie{3/minimalbeispiel.tex}
-%\folie{3/minimalpolynom.tex}
+\folie{3/motivation.tex}
+\folie{3/inverse.tex}
+\folie{3/polynome.tex}
+\folie{3/division.tex}
+\folie{3/division2.tex}
+\folie{3/ringstruktur.tex}
+\folie{3/teilbarkeit.tex}
+\folie{3/faktorisierung.tex}
+\folie{3/faktorzerlegung.tex}
+\folie{3/einsetzen.tex}
+\folie{3/maximalergrad.tex}
+\folie{3/minimalbeispiel.tex}
+\folie{3/minimalpolynom.tex}
\folie{3/drehmatrix.tex}
\folie{3/drehfaktorisierung.tex}
\folie{3/operatoren.tex}