Author: Panagiotis
10
Okt
In
[1, p. 60 exercise 3.1] a

real random vector

is given , which is distributed according to a multivatiate Gaussian PDF with zero mean and covariance matrix:
We are asked to find

if

where

is given by the relation:
so that

and

are uncorrelated and hence independent. We are also asked to find the Cholesky decomposition of

which expresses

as

, where

is lower triangular with 1′s on the principal diagonal and

is a diagonal matrix with positive diagonal elements.
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