TUD_MATH_BA/Material/orthogonaler_UVR.tex
Henry Haustein 3fc77dc780 kleines Bild zu Annulator und orthogonales Komplement
war im Fischer ganz gut verständlich
2018-08-06 19:41:45 +02:00

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\documentclass{report}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{amssymb}
\begin{document}
\begin{center}\begin{tikzpicture}
\draw[blue] (2.75,-2) -- (2.75,3);
\node[blue] at (3.2,3) (Komp) {$U^\perp$};
\draw[thick] (0,0) -- (4,0);
\draw[thick] (0,0) -- (1.5,1.5);
\draw[thick] (4,0) -- (5.5,1.5);
\draw[thick] (1.5,1.5) -- (5.5,1.5);
\node at (3.5,0.4) (U) {$U$};
\node at (0,2.5) (R) {$\mathbb{R}^3$};
\coordinate (c2) at (2.75,0.75);
\draw ($(c2) + (0:0.4)$) arc (0:90:0.4); % radius=4mm, initial=0, final=90
\draw[thick] (2.90,0.90) circle (0.01);
\end{tikzpicture}\end{center}
\begin{center}\begin{tikzpicture}
\draw[->] (-7,0) -- (-1,0);
\draw[->] (-4,-3) -- (-4,3);
\draw[thick] (-7,-1.5) -- (-1,1.5);
\draw[fill=black] (-3,0.5) circle (0.05);
\node at (-5,2) (real) {$\mathbb{R}^2$};
\node at (-1,1.8) (gerade) {$L$};
\node at (-1.7,0.5) (punkt) {$x=\left(\begin{array}{c}x_1 \\ x_2\end{array}\right)$};
\draw[->] (1,0) -- (7,0);
\draw[->] (4,-3) -- (4,3);
\draw[thick] (2.5,3) -- (5.5,-3);
\draw[fill=black] (4.5,-1) circle (0.05);
\node at (5,2) (real) {$\left(\mathbb{R}^2\right)^*$};
\node at (2.2,3) (annulator) {$L^0$};
\node at (5.7,-1) (punkt2) {$a=(a_1,a_2)$};
\end{tikzpicture}\end{center}
\end{document}