Question: 3. A symmetric matrix S = ST has orthonormal eigenvectors ,...,Un. Then any vector a can be written as a combination z = Cv

3. A symmetric matrix S= ST has orthonormal eigenvectors ,...,Un. Then any vector x can be written as a

3. A symmetric matrix S = ST has orthonormal eigenvectors ,...,Un. Then any vector a can be written as a combination z = Cv + + cnun. Explain these two formulas: rx = ++ xSx=Aci+.... +Anc. 4. Problem 3 gives a neat form for the Rayleigh quotient: x Sx__ \ + r Ac+ = + Why is the maximum value of that ratio equal to the largest eigenvalue A? R(x) = ... +Anch +c

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