(a) Prove that if is an eigenvalue of A, then n is an eigenvalue of An....

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(a) Prove that if λ is an eigenvalue of A, then λn is an eigenvalue of An.
(b) State and prove a converse if A is complete. (The completeness hypothesis is not essential, but this is harder, relying on the Jordan canonical form.)

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 09:06 AM

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(a) Prove that if is an eigenvalue of A, then n is an eigenvalue of An....

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a If Av v then by induction A n v n v and hence v is an eigenvector wit...View the full answer

Applied Linear Algebra

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