Endomorphism/Eigenvalue/Geometric multiplicity/Definition

Geometric multiplicity

Let ${}K$ be a field, ${}V$ a ${}K$-vector space and

$\varphi \colon V\longrightarrow V$

a linear mapping. For ${}\lambda \in K$ we call

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

the geometric multiplicity of ${}\lambda$.