Let A be a Hermitian matrix with eigenvalues 1 2 n and orthonormal eigenvectors u1, ..
Chapter 6, Problem 28(choose chapter or problem)
Let A be a Hermitian matrix with eigenvalues 1 2 n and orthonormal eigenvectors u1, ... , un. For any nonzero vector x in Rn, the Rayleigh quotient (x) is defined by (x) = Ax, x x, x = xHAx xHx (a) If x = c1u1 ++ cnun, show that (x) = |c1| 21 + |c2| 22 ++|cn| 2n c2 (b) Show that n (x) 1 (c) Show that max x=0 (x) = 1 and min x=0 (x) = n
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