Let A be an n x n real matrix with the property that AT A Show that if Ax x for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A ...

x T Ax x T x x T because x is an eigenvector It is easy to see ...

Let A be an n x n real matrix with the property that AT = A. Show

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Let A be an n x n real matrix with the property that AT = A. Show that if Ax = λx for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A.

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Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

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Question Posted: May 02, 2016 12:07 PM

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Let A be an n x n real matrix with the property that AT = A. Show

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x T Ax x T x x T because x is an eigenvector It is easy to see ...View the full answer

Linear Algebra and Its Applications

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