Definitions. A linear operator T on a vector space V is called nilpotent if Tp= T0 for some positive integer p. An n×n matrix A is called nilpotent if Ap= O for some positive integer . Give an example of a linear operator T on a finite-dimensional vector space such that T is not nilpotent, but zero is the only eigenvalue of T. Characterize all such operators.

Definitions. A linear operator T on a vector space V is called nilpotent if Tp= T0 for some positive integer p. An n×n matrix A is called nilpotent if Ap= O for some positive integer . Give an example of a linear operator T on a finite-dimensional vector space such that T is not nilpotent, but zero is the only eigenvalue of T. Characterize all such operators.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.5: Applications

Problem 30EQ

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