\begin{definition}[Definition:Eigenvector/Linear Operator]
Let $K$ be a field.
Let $V$ be a vector space over $K$. 
Let $A : V \to V$ be a linear operator.
Let $\lambda \in K$ be an eigenvalue of $A$.
A non-zero vector $v \in V$ is an '''eigenvector corresponding to $\lambda$''' {{iff}}:
:$v \in \map \ker {A - \lambda I}$
where: 
:$I : V \to V$ is the identity mapping on $V$
:$\map \ker {A - \lambda I}$ denotes the kernel of $A - \lambda I$.
That is, {{iff}}: 
:$A v = \lambda v$
\end{definition}