Endomorphism/Geometric and algebraic multiplicity/Fact

Let $K$ denote a field, and let $V$ denote a finite-dimensional vector space. Let

$\phi :V⟶V$

denote a linear mapping and $\lambda \in K$.

Then we have the estimate

${\dim }_K\left({\mathrm{Eig}}_{\lambda }\left(\phi \right)\right)\le {\mu }_{\lambda }(\phi )$

between the geometric and the

algebraic multiplicity.

Proof, Write another proof