In reply to Imre Polik.

Yes, it is possible, since each x`*x is PSD, but I don't see it as very helpful. A primary purpose for wanting to create a large PD matrix is so that you can can simulate vectors from MVN (or other multivariate distribution). If you form a PSD matrix by using n linearly independent vectors, how do you obtain those vectors? If you choose independent vectors, the correlation matrix will always be close to the identity matrix, which isn't very interesting. In general, for arbitrary vectors, you won't be able to predict what the correlation matrix will look like. The article's method enables you to specify the values of the correlation matrix, which is a powerful property to control.