16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.4.12

Elementary Canonical Forms

Mathematics — Linear Algebra · characteristic-values-polynomial-of-operator

Problem

Let

T

be a linear operator on a finite-dimensional vector space over an algebraically closed field

F

. Let

f

be a polynomial over

F

. Prove that

c

is a characteristic value of

f(T)

if and only if

c = f(t)

, where

t

is a characteristic value of

T