Recall the covariance of two random variables X and Y is defined as Cov(X, Y) = E[(X − E[X])(Y − E[Y])]. For a multivariate random variable Z (i. e., each index of Z is a random variable), we define the covariance matrix Σ such that Σi j = Cov(Zi , Zj). Concisely, Σ = E[(Z − µ)(Z − µ) > ], where µ is the mean value of the random column vector Z. Prove that the covariance matrix is always positive semidefinite (PSD).