Endomorphism/Geometric and algebraic multiplicity/Fact

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

$\varphi \colon V\longrightarrow V$

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

Then we have the estimate

${}\dim _{K}{\left(\operatorname {Eig} _{\lambda }{\left(\varphi \right)}\right)}\leq \mu _{\lambda }(\varphi )\,$

between the geometric and the

algebraic multiplicity.

Proof, Write another proof