Page "Multivariate normal distribution" Paragraph 14

The covariance matrix is allowed to be singular ( in which case the corresponding distribution has no density ).

This case arises frequently in statistics ; for example, in the distribution of the vector of residuals in the ordinary least squares regression.

Note also that the X < sub > i </ sub > are in general not independent ; they can be seen as the result of applying the matrix A to a collection of independent Gaussian variables z.