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