Question: An n-dimensional Gaussian vector W has a block diagonal covariance matrix where C X is m à m, C Y is (n m) à (n

An n-dimensional Gaussian vector W has a block diagonal covariance matrix

[Cx %3D CY Cw

where CX is m × m, CY is (n €“ m) × (n €“ m). Show that W can be written in terms of component vectors X and Y in the form

An n-dimensional Gaussian vector W has a block diagonal covariance

such that X and Y are independent Gaussian random vectors.

[Cx %3D CY Cw

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