latex-pictures

A collection of TikZ drawings and other images 🖌️

dihedral-representation-is-irreducible.tikz (664B)

 1 % An ilustration of the proof that the representation of the Dihidral group is
 2 % irreducible
 3 % Copyright Pablo (C) 2021
 4 \begin{tikzpicture}[scale=1.2]
 5     % The axis
 6     \draw[->] (-1,0)--(3,0) node[right]{$x$};
 7     \draw[->] (0,-0.5)--(0,1.5) node[above]{$y$};
 8     
 9     % sigma
10     \draw[->] (1.5,0.3) arc (0:50:1cm) node at (1.7,0.85) {$\sigma$};
11 
12     % A non-zero vector v
13     \filldraw[black] (1.5, 0.3) circle (1pt);
14     \node[right] at (1.5, 0.3) {$v$};
15 
16     % sigma(v)
17     \filldraw[black] (1, 1.15) circle (1pt);
18     \node[left] at (1, 1.15) {$\sigma \cdot v$};
19     
20     % The subspace spaned by v
21     \draw[dotted] (-1, -0.2)--(3, 0.6);
22 \end{tikzpicture}