Let A be a symmetric matrix. (a) Show that An is symmetric for any nonnegative integer n.

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Let A be a symmetric matrix.
(a) Show that An is symmetric for any nonnegative integer n.
(b) Show that 2A2 - 3A + I is symmetric.
(c) Show that any matrix polynomial p(A) of A, cf. Exercise 1.2.35, is a symmetric matrix.

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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 08:25 AM

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Let A be a symmetric matrix. (a) Show that An is symmetric for any nonnegative integer n.

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a Since A is symmetric we have A n T AA A T A T A T A T ...View the full answer

Applied Linear Algebra

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