I am trying to proof whether the SemiCovariance matrix defined in equation (5) from the following paper http://web.iese.edu/jestrada/PDF/Research/Refereed/MSO.pdf is positive definite or not.
As a starting point, I was thinking about using the whole covariance matrix, which is positive definite and then split it into the SemiCovariance and the rest. But from there I am stuck.
I appreciate your help.
Best, Jc