Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 7 - Eigenvalues and Eigenvectors - 7.6 Jordan Canonical Forms - True-False Review - Page 486: e

Answer

True

Work Step by Step

The given statement is a part of Definition 7.6.1. If $p$ is the smallest positive integer such that $(A − λI)p v = 0$, then the vector $(A − λI)^{p−1}v$ is a (regular) eigenvector of $A$ corresponding to $λ$, since it belongs to the null space of $A − λI$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.