mirror of
https://github.com/vale981/TUD_MATH_BA
synced 2025-03-06 01:51:38 -05:00
86 lines
2.4 KiB
TeX
86 lines
2.4 KiB
TeX
\documentclass[a4paper, 12pt]{article}
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\usepackage{mathtools}
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\usepackage{amssymb}
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\usepackage[utf8]{inputenc} % special characters
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% diagramms
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\usepackage{tikz} %diagrams
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\usetikzlibrary{arrows,cd,calc} % for commutative diagrams
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% template for a simple article in maths, also useful to just type up something math short!
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%\newcommand{\invf}{f^{-1}}
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%\newcommand{\invg}{g^{-1}}
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%opening
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\title{}
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\author{}
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\date{\today}
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\begin{document}
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\maketitle
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\begin{center}
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\begin{tikzpicture}
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\node (V) at (0,0) {$V$};
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\node (W) at (3,0) {$W$};
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\node (R) at (1.5,-1.5) {$V\slash U$};
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\draw[->, above] (V) to node {$f$} (W);
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\draw[->, below] (V) to node {$\pi_U$} (R);
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\draw[->, right, dashed] (W) to node {$\tilde f$} (R);
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\end{tikzpicture}
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\end{center}
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\begin{center}
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\begin{tikzpicture}
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\node (V) at (0,0) {$V$};
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\node (W) at (3,0) {$W$};
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\node (R) at (1.5,-1.5) {$V\slash U$};
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\draw[->, above] (V) to node {$f$} (W);
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\draw[->, below] (V) to node {$\pi_U$} (R);
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\draw[->, right, dashed] (W) to node {$\tilde f$} (R);
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\end{tikzpicture}
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\end{center}
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\begin{center}
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\begin{tikzcd}
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V \arrow[r, "f"] \arrow[dr, dashrightarrow, "f^{\ast}(\phi)"]
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& W \arrow[d, "\phi"]\\
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& K\\
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V^{\ast} & \arrow[l, "f^{\ast}"] W^{\ast}
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\end{tikzcd}
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\end{center}
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\begin{center}
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\begin{tikzcd}
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V \arrow[r, "f"] \arrow[d, "\iota_V \cong"]
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& W \arrow[d, "\iota_W \cong"] \\
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V^{\ast \ast} \arrow[r, "f^{\ast \ast}"]
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& W^{\ast \ast}
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\end{tikzcd}
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\end{center}
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\begin{center}
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\begin{tikzpicture}[scale=0.6]
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\draw[thick] (-2,0) -- (10,0) node[right] {$x_1$};
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\draw[thick] (0,-2) -- (0,10) node[above] {$x_2$};
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\coordinate (center) at (0,0)
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% triangle
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%\fill[line width=1pt, color=red,fill=red, opacity=0.1] (0,0) -- (2,7) -- (7,2) -- cycle ;
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\draw[red] (2,7) -- (7,2);
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\draw[fill=green] ($(center) + (0:5)$) arc (0:12:5)
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\draw[red] (3.5,3.5) node {\scriptsize $\Delta$};
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%Circles
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\draw[shift={(-7.8,-4.5)}, color=green, opacity=0.1, fill=green] (0,0) -- (0:5.6) arc (0:7.2:5.6) -- cycle
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% Paralello
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\draw[->, thick] (0,0) -- (7,2) node[right] {\scriptsize $x_1=(a,b)$};
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\draw[->, thick] (0,0) -- (2,7) node[above] {\scriptsize$x_2=(c,d)$};
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\draw[->, thick] (7,2) -- (9,9) node[right] {\scriptsize$x_1 + x_2$};
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\draw[->, thick] (2,7) -- (9,9);
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\draw[blue] (0,0) -- (7,2) node[near end, below] {\scriptsize $g_{\Delta}$};
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\draw[blue] (3.5,1) -- (2,7) node[near start, right] {\scriptsize$h_{\Delta}$};
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\end{tikzpicture}
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\end{center}
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\end{document}
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