In this exercise we investigate an alternative approach to checking that the eigenvalues of an N× N symmetric matrix C (e.g., a Hessian matrix) are all nonnegative. This approach does not involve explicitly computing the eigenvalues themselves, and is significantly easier to employ in practice. Let C be anN×N symmetric matrix. Show that if C has all nonnegative eigenvalues then the quantity zTCz ≥ 0 for all z. Hint: use the eigenvalue decomposition of C

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