I want to prove that for every divisor $p$ of $m_f$, minimal polynomial of the linear application $f:V \to V$, I can find a vector $v \in V$ that $p=m_{f,v}$, minimal polynomial of that vector.
My idea was to use the Cyclic Decomposition Theorem, but I couldn't find the right way to use it. And I'm not sure if it works for any vector space or only for a f-cyclic one. Can anybody give some hint? Thanks.