Why is the Haar measure times the volume of the eigenvalue simplex considered a good measure of Hilbert space volume?
In particular, why do we need both of these to find the volume? And should I be thinking of it as an actual volume or not? This Hilbert space volume is talked about in this paper. It says There ...
I have an approximately basketball-sized non-hollow piece of aluminum sitting in my house that is of irregular shape. I need to find the volume of it for a very legitimate yet irrelevant reason. ...