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added jordan normal form

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Martin Thoma 2012-08-15 15:03:35 +02:00
parent 2d7f2ff7c5
commit 5c57d6808a
5 changed files with 130 additions and 0 deletions
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32
tikz/jordan-normal-form-block/Makefile Normal file
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SOURCE = jordan-normal-form-block
DELAY = 80
DENSITY = 300
WIDTH = 500
make:
pdflatex $(SOURCE).tex -output-format=pdf
pdflatex $(SOURCE).tex -output-format=pdf
make clean
clean:
rm -rf $(TARGET) *.class *.html *.log *.aux
gif:
pdfcrop $(SOURCE).pdf
convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
make clean
png:
make
make svg
inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
transparentGif:
convert $(SOURCE).pdf -transparent white result.gif
make clean
svg:
#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
pdf2svg $(SOURCE).pdf $(SOURCE).svg
# Necessary, as pdf2svg does not always create valid svgs:
inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

44
tikz/jordan-normal-form-block/jordan-normal-form-block.tex Normal file
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\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{fit,matrix,positioning}
\tikzset{%
highlight/.style={
rectangle,
rounded corners,
fill=#1!15,
draw,
fill opacity=0.5,
%thick,
inner sep=1pt
}
}
\newcommand{\tikzmark}[2]{
\tikz[overlay,remember picture,baseline=(#1.base)] \node (#1) {#2};
}
\newcommand{\Highlight}[3]{%
\tikz[overlay,remember picture]{
\node[highlight=#3,fit=(#1.north west) (#2.south east)] {};}
}
\begin{document}
\begin{preview}
$
A_{\lambda_i} =
\left(
\begin{array}{*5{c}}
\tikzmark{1}{$\lambda_i$} & 1 & 0 & & 0 \\
& \lambda_i & 1 & & \\
& & \lambda_i\tikzmark{2}{} & & \\
& & & \ddots & \\
0 & & & & \tikzmark{3}{$\lambda_i$} \tikzmark{4}{} \\
\end{array}
\right)
\Highlight{1}{2}{blue}
\Highlight{3}{4}{red}
$
\end{preview}
\end{document}

32
tikz/jordan-normal-form/Makefile Normal file
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SOURCE = jordan-normal-form
DELAY = 80
DENSITY = 300
WIDTH = 500
make:
pdflatex $(SOURCE).tex -output-format=pdf
pdflatex $(SOURCE).tex -output-format=pdf
make clean
clean:
rm -rf $(TARGET) *.class *.html *.log *.aux
gif:
pdfcrop $(SOURCE).pdf
convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
make clean
png:
make
make svg
inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
transparentGif:
convert $(SOURCE).pdf -transparent white result.gif
make clean
svg:
#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
pdf2svg $(SOURCE).pdf $(SOURCE).svg
# Necessary, as pdf2svg does not always create valid svgs:
inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

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tikz/jordan-normal-form/jordan-normal-form.pdf Normal file
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22
tikz/jordan-normal-form/jordan-normal-form.tex Normal file
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\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{fit,matrix,positioning}
\begin{document}
\begin{preview}
$
J =
\left(
\begin{array}{*4{c}}
A_{\lambda_1} & & & 0\\
& A_{\lambda_2} & & \\
& & \ddots & \\
0 & & & A_{\lambda_k}
\end{array}
\right)
$
\end{preview}
\end{document}