Is there a probabilistic or analytical meaning of the eigenvalues/eigenvectors of covariance matrix of multivariate normal distribution?
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The accepted answer to the question at http://math.stackexchange.com/questions/23596/why-is-the-eigenvector-of-a-covariance-matrix-equal-to-a-principal-component may be of help here. – Kevin P. Costello Feb 01 '13 at 21:31