Right. So assuming no restriction is imposed on their correlation, ##a = 1## and W is true and assuming variables are totally uncorrelated, ##a = 0## diagonal matrix of diag(W) is true. I need to figure out how to specify ##a## in my case.
You are right — changing only the diagonal of the covariance matrix would not transform the matrix and it would not be the covariance matrix of the variables anymore. I will try to explore the possibility of a convex combination of the full matrix W and matrix with only diag(W). Something like...
I have a variance-covariance matrix W with diagonal elements diag(W). I have a vector of weights v. I want to scale W with these weights but only to change the variances and not the covariances. One way would be to make v into a diagonal matrix and (say V) and obtain VW or WV, which changes both...