Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card
8th Edition
ISBN: 9781337131216
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 7.2, Problem 46E

Guide Proof Prove nonzero nilpotent matrices are not diagonalizable

Getting started: From Exercises 80 in Section 7.1, you know that 0 is the only eigenvalue of the nilpotent matrix A. Show that it is impossible for A to be diagonalizable.

(i) Assume A is diagonalizable, so there exists an invertible matrix P such that P − 1 A P = D , here D is the zero matrix.

(ii) Find A in term of P , P − 1 and D.

(iii) Find a contradiction and conclude that nonzero nilpotent matrices are not diagonalizable.

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Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card

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