Kunze Linear Algebra · Problem 7.2.6

Rational and Jordan Forms

Mathematics — Methods · t-annihilator

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.