Gaussian
The multivariate Gaussian PDF of dimension with mean
and covariance
is:

(16.3) 
For independent zeromean samples of variance 1, this simplifies to
Note that if we know the eigendeomposition of , we may write (16.3)
in a simpler form. Since is a symmetric positive definite matrix,
the eigenvectors form a complete orthogonal subspace on
. Let
be the eigendecomposition of . Let the matrix be formed from the columns
. Let
The covariance matrix of
is clearly the diagonal matrix
formed from the eigenvalues
. Therefore
the above formula simplifies to
Baggenstoss
20170519