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what is the solution for max y$^T$ $\Sigma$ y in terms of maximum eigen value and the associated eigen vectors ?

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    The maximum is usually infinity. However, if you restrict yourself to unit vectors and $\Sigma$ is symmetric, the maximum is the largest eigenvalue of $\Sigma$, with the corresponding eigenspace as maximizers.2011-02-23
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    @Yuval: I think that you should consider changing your comment to an answer so that this isn't an 'unanswered' anymore. It's sufficient, I think. I suppose you could suggest a proof as well.2011-06-02

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