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How to find a covariance matrix from given mean values. e.g. Given mean values m1= (1/4) (3 1 1)T and m2 = (1/4) (1 3 3)T

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What do you mean by "mean values"? You can not determine the covariance matrix given only the means of two random vectors. (The covariance matrix could be any nonnegative definite matrix.) –  passerby51 May 13 '12 at 4:34
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You need the original observations to get covariance terms because a variance sums (Xi - Xs sample mean)^2 terms and covariances sum terms like (Xi-Xs sample mean) (Yi-Ys sample mean). If you have two multivariate distributions then there would be two such covariance matrices to compute or one pooled one if you assume the two distributions have the same covariance matrix.

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