Sometimes we want to test a model with some random data. When dealing with quadratic problems we may need to invent a positive definite matrix \(Q\). One simple way to do this is as follows:
I.e. in matrix terms: \(Q:=Q^TQ\) (i.e. the assignment above is not done one-by-one but rather in parallel). To be precise: \(Q\) will be positive semi-definite, i.e. \(x^TQx\ge 0\).
This simple device can help generating random data for convex quadratic models.