I need to prove the following but I don't know how:
Admit Y ~ N($\mu$,$U^t$$\Sigma$U) where $\Sigma$ is a diagonal matrix containing positive elements and U is a unitary matrix.
Show that UY ~ N(U$\mu$,$\Sigma$)
Should I proceed using the Gaussian multivariate definition or there is a quicker way of solving it?
Thank you very much in advance.
James
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