Endomorphism/Finite-dimensional/Minimal polynomial/Principal ideal/Fact

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

f\colon V\longrightarrow V

Then the set

{\left\{P\in K[X]\mid P(f)=0\right\}}

is a principal ideal in the polynomial ring ${}K[X]$ , which is generated by the minimal polynomial

{}\mu _{f}

.