8. Show all the steps clearly please 8. A linear operator T: V → V is called nilpotent if TP = 0 for certain positive integer p.Prove that if an operator is nilpotent then 0 is its only eigenvalue.R3 defined by I (r) - Ar for r column vectors in6For the linear operator I1. D3

Given that T:V→V is linear operator. A linear operator T:V→V is called nilpotent if Tp=0 for certain…

Answered: A linear operator T: V→V is called…

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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A linear operator T: V→V is called nilpotent if TP = 0 for certain positive integer p. Prove that if an operator is nilpotent then 0 is its only eigenvalue.