.) 12. Let A be the companion matrix of a monic polynomial g(x) = c + + + C-12"-1+2 with coefficients in the field F, and let AT be the transpose of A. Show that (even though ATA) the rational canonical form of AT over F is equal to A.

.) 12. Let A be the companion matrix of a monic polynomial g(x) = c + + + C-12"-1+2 with coefficients in the field F, and let AT be the transpose of A. Show that (even though ATA) the rational canonical form of AT over F is equal to A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 24EQ

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Question

.) 12. Let A be the companion matrix of a monic polynomial
g(x) = c + + + C-12"-1+2
with coefficients in the field F, and let AT be the transpose of A. Show that (even though ATA) the
rational canonical form of AT over F is equal to A.

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