One of the questions on the course involves finding the angle and axis of this rotation matrix;
$$R = \gamma\ \begin{pmatrix} 0 & -2 & 1\\ 2 & 0 & 0\\ -1 & 0 & 0 \end{pmatrix}$$
My lecturer solves this in an example that reads;
$$ \omega_i = -\frac{1}{2} \epsilon_{ijk}R_{jk} $$
$$ \omega_i = (R_{23},R_{31},R_{12})_i = \omega n_i $$
Therefore the angle is $|\underline{\omega}| = \sqrt{5} \gamma$ and axis is $ \underline{n} = \frac{1}{\sqrt{5}}(0,1,2)$
Two questions;
- What is $\omega$?
- Is this method limited to this case or can it be applied generally?