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

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3. A symmetric matrix S = ST has orthonormal eigenvectors ₁,...,Un. Then any vector a can be written as a combination z = C₁v₁ + + cnun. Explain these two formulas: r²x = ² ++ xSx=A₁ci+.... •+Anc². 4. Problem 3 gives a neat form for the Rayleigh quotient: x²¹ Sx__ \₁² + r A₁c²+ = + Why is the maximum value of that ratio equal to the largest eigenvalue A₁? R(x) = ... +Anch +c² 3. A symmetric matrix S = ST has orthonormal eigenvectors ₁,...,Un. Then any vector a can be written as a combination z = C₁v₁ + + cnun. Explain these two formulas: r²x = ² ++ xSx=A₁ci+.... •+Anc². 4. Problem 3 gives a neat form for the Rayleigh quotient: x²¹ Sx__ \₁² + r A₁c²+ = + Why is the maximum value of that ratio equal to the largest eigenvalue A₁? R(x) = ... +Anch +c²

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First formula r c 1 1 2 2 r One u one one c two two u two two c n u n Here r represents any vector 1 ... View the full answer