can be derived if we
first orthogonalize the features.
which can also be written
This is the energy in orthogonal to the columns
of . Accordingly, is statistically independent
of under .
is chi-squared with degrees of freedom,
is the Gaussian distribution
with mean and co-variance
can be obtained from using
a linear transformation with Jacobian of determinant 1,
we can write
The J-function is just
For more information see the function