16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.6

The Rational and Jordan Forms

Mathematics — Linear Algebra · t-annihilators

Problem

Let

T

V

, and

F

be as in Exercise 5. Suppose

\alpha

and

\beta

are vectors in

V

which have the same

T

-annihilator. Prove that, for any polynomial

f

, the vectors

f\alpha

and

f\beta

have the same

T

-annihilator.