Cayley-Hamilton/Minimal polynomial and characteristic polynomial/Fact

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

$f\colon V\longrightarrow V$

be a linear mapping.

Then the

characteristic polynomial ${}\chi _{f}$ is a multiple of the minimal polynomial

${}\mu _{f}$ of ${}f$.

Proof, Write another proof