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Le us create N independent and identitcally distributed (iid) normal random vectors with zero mean and specific covariance matrix. Each vector is of size p. Let $\Sigma$ be the specific covariance matrix.

    p = 20;
    N = 50;
    M = chol($\Sigma$)
    Matr =  M' * randn(p, N) 

In fact I want to know why in all references, they use chol?. Why they don't simply write Matr = randn(N, p) * ($\Sigma$) ? So what is the advantage of chol (or cholcov) in this case?

I made some results, and I noticed that they significantly differ when I remove the chol !! Even it takes more time for the computation..why??

Any help will be very appreciated!

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