Q: properties of covariance matrices

From: KY (kky2001_at_columbia.edu)
Date: 10/28/04 

Date: 27 Oct 2004 22:14:08 -0700

Let x and y be n-tuplets of normally distributed random variables, and let
   C = cov(x,y') be the nxn covariance matrix of x and y.

Let z be some fixed n-tuplet whose elements are all strictly positive.

 1) Are all the elements of the n-vector, Cz, non-negative?
 2) Is z'Cz > 0?

 Where can I read more about bounds on the elements of covariance matrices?

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