% An ilustration of the proof that the representation of the Dihidral group is
% irreducible
% (C) Thiago Brevidelli
\begin{tikzpicture}[scale=1.2]
    % The axis
    \draw[->] (-1,0)--(3,0) node[right]{$x$};
    \draw[->] (0,-0.5)--(0,1.5) node[above]{$y$};
    
    % sigma
    \draw[->] (1.5,0.3) arc (0:50:1cm) node at (1.7,0.85) {$\sigma$};

    % A non-zero vector v
    \filldraw[black] (1.5, 0.3) circle (1pt);
    \node[right] at (1.5, 0.3) {$v$};

    % sigma(v)
    \filldraw[black] (1, 1.15) circle (1pt);
    \node[left] at (1, 1.15) {$\sigma \cdot v$};
    
    % The subspace spaned by v
    \draw[dotted] (-1, -0.2)--(3, 0.6);
\end{tikzpicture}
