Hi Rick, this is a nice article. Could you introduce some other methods to implement the transformation between uncorrelated variables to correlated variables? I mean Cholesky is an efficient way to do this, but I am wondering whether there is another way more convenient than it. Now I have a big-size original sample matrix of several correlated variables and I do separated sampling for every single variable (by using Latin hypercube sampling perhaps). Thus I can get a sample matrix (called A) in which the samples are not correlated. I know I can permute those samples subjected to Σ by using Cholesky. Is that the only way to make A get the correlation?