The covariance matrix in (2.63) is a positive definite and symmetric matrix which can decomposed into:
where is a lower triangular matrix:
A random vector with a multinormal jpdf can be generated from:
where is a normal vector of independent zero mean and one standard deviation normal deviates, and is the vector of means.
The decomposition can be performed using the so-called square root method [88] which is based on a set of recursive formulae for the computation of the elements of :