# Minimal polynomial, transpose, similar

## Homework Statement

a) Prove that if a polynomial f(lambda) has f(A)=0, then f(AT)=0

b) Prove that A and AT have the same minimal polynomial.

c) If A has a cyclic vector, prove that AT is similar to A.

2. The attempt at a solution

a) I know that I need to show that f(AT) = f(A)T.

b) The main problem is that I don't think I understand completely what the minimal polynomial is. I know how to get the minimal polynomial from the last column of a matrix in rational canonical form, and that's about it.

c) This should be a direct consequence of part (b) since same minimal polynomial --> similar.