Problem 8 Let T be a linear operator on a vector space V, and let x be an eigenvector of T corresponding to the eigenvalue X. For any positive integer m, prove that x is an eigenvector of Tm corresponding to the eigenvalue Xm
Problem 8 Let T be a linear operator on a vector space V, and let x be an eigenvector of T corresponding to the eigenvalue X. For any positive integer m, prove that x is an eigenvector of Tm corresponding to the eigenvalue Xm
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Problem 8
Let \( T \) be a linear operator on a vector space \( V \), and let \( x \) be an eigenvector of \( T \) corresponding to the eigenvalue \( \lambda \). For any positive integer \( m \), prove that \( x \) is an eigenvector of \( T^m \) corresponding to the eigenvalue \( \lambda^m \).
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