My question is about how to compute the Haar measure for O(n) and U(n) groups.
For example, for the conventional parametrization of SO(3) with 3 angels, the Haar measure is
$ dO= cos(\theta_{13})*d\theta_{12}*d\theta_{13}*d\theta_{23}$ .
How one derives this formula? I want to compute the Haar measure for both O(n) and U(n) for general n.
I am a student of physics and I am not quite familiar with Haar measure.
You might like these lecture notes. In particular, the second page discusses such calculations.