I have a rather simple question but googling it did not bring a satisfactory result:
Assume you have given two function $f$ and $g$ on some space $\mathcal{L}^2(\Omega)$ where $\Omega \subset \mathbb{R}^n$. I am looking for the angle between the functions.
Is $~\cos(\alpha) = \dfrac{\langle f, g\rangle}{\|f\|\|g\|}~$ already the formula I am looking for? I know that this is the formula for the angle between subspaces. If I assume I look at the two subspaces $\operatorname{span}(f)$ and $\operatorname{span}(g)$ than all should work out...
Thanks for help!