In reply to Knut.

This post is almost 13 years old, so I cannot remember what I might have been thinking back then. I cannot locate a follow-up post. When I think about this problem today, the case of a correlation matrix seems harder than the covariance case. I do not see an easy way to construct a correlation matrix with a specified set of eigenvalues (which must sum to n for an nxn matrix). You cannot merely use the spectral decomposition and try to construct Q`*diag(lambda)*Q because that matrix is not likely to be a correlation matrix with 1s on the diagonal. In short, I think my statement is wrong, which is why there was no follow-up post. Sorry about that.