Hi everyone,

I am looking for a way of simulating correlation matrices of fixed dimension in (at least) two ways. 

First, I would like to determine the "uniform" distribution over the "correlation matrices space" and being able to sample from it (even defining what "uniform" means is not such an easy task !!!).

Second, I would like to get some parametric law for which sampled correlation matrices would be such that :

-the expectations of the eigenvalues are equal to some fixed set of values.
 
-we have a certain amount of "control" over the second moments of those eigenvalues through the parameters set.

I hope I made myself clear enough, and thank's for any leads or references to acheive such a thing. From my point of view this is a surprisingly complex problem and I thought it might raise some interest among you. 

So far I tried an approach using diagonalization through orthogonal matrices and eigenvalues which was not really a success...

Regards