Minimal polynomial and characteristic polynomial/Same zeroes/Fact

Let ${\displaystyle {}V}$ be a finite-dimensional vector space over a field ${\displaystyle {}K}$, and let

${\displaystyle f\colon V\longrightarrow V}$

be a linear mapping.

Then the

characteristic polynomial ${\displaystyle {}\chi _{f}}$ and the minimal polynomial

${\displaystyle {}\mu _{f}}$ have the same zeroes.