(a) Show that, for any square matrix A, AT and A have the same characteristic polynomial and...

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(a) Show that, for any square matrix A, AT and A have the same characteristic polynomial and hence the same eigenvalues.
(b) Give an example of a 2 × 2 matrix A for which AT and A have different eigenspaces.

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Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

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Question Posted: Apr 15, 2016 06:13 AM

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(a) Show that, for any square matrix A, AT and A have the same characteristic polynomial and...

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a Since I T I T I we have A T I A T I T A I T So that using Theorem 410 detA T I det A I T detA I ...View the full answer

Linear Algebra A Modern Introduction

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