16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.3.5

Elementary Canonical Forms

Mathematics — Linear Algebra · nilpotent-operator

Problem

Let

V

be an

n

-dimensional vector space and let

T

be a linear operator on

V

. Suppose that there exists some positive integer

k

so that

T^k = 0

. Prove that

T^n = 0