Let A be a Hermitian matrix with eigenvalues Î»1 ¥ Î»2 ¥ ... ¥ Î»n and orthonormal

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Let A be a Hermitian matrix with eigenvalues Î»1 ‰¥ Î»2 ‰¥ ... ‰¥ Î»n and orthonormal eigenvectors u1,...,un. For any nonzero vector x in Cn the Rayleigh quotient p(x) is defined by

(a) If x = c1u1 + ... + cnun show that

(b) Show that
Î»n ‰¤ p(x) ‰¤ Î»1

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Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

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Question Posted: Jun 13, 2016 01:02 AM

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Let A be a Hermitian matrix with eigenvalues Î»1 ¥ Î»2 ¥ ... ¥ Î»n and orthonormal

Question:

ρ(x) = (Ax, x) = X"AX

Step by Step Answer:

a Since the eigenvectors u 1 u n form an orthonormal b...View the full answer

Linear Algebra with Applications

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