Consider a random vector X e RP with mean EX is a p x p dimensional...

Question

Question

Consider a random vector X e RP with mean EX is a p x p dimensional matrix. Denote the jth eigenvalue and jth eigenvector of

math Advanced-Math

Answer 1

Answer #1

The covariance matrix $Cov X] E(X - E[X]) (X - EX$ .

It is given the $EX0$ . But $EZ EpX= pE[X] = 0$ (Since expectation is linear)

Where $(1, 2,.$ is made up of orthonormal vectors of $\Sigma$ .

Now $= E[X X| z=Cov[Z] EZZ= E[pXX*$

$= \varphi^t \Sigma \varphi = \varphi^t \big( \lambda_1 \phi_1, \lambda_2 \phi_2, \dots , \lambda_p \phi_p \big)$

$0 0 2 0 0 Ap 0 0$

Answer 2

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