1 dimensional example
BurgerŐs equation
2K+1 independent degrees of freedom define u on 2K+1 points
on a circle. Defines a random vector u(n) with  sample covariance
                                     U(n,m)=<u(n)u(m)>
                  Because of sampling U is a random matrix.
Given by orthogonal projection
Multiply eqn by exp(-ikx) and integrate