\begin{definition}[Definition:Eigenvalue/Linear Operator]
Let $K$ be a field.
Let $V$ be a vector space over $K$. 
Let $A : V \to V$ be a linear operator.
$\lambda \in K$ is an '''eigenvalue''' of $A$ {{iff}}:
:$\map \ker {A - \lambda I} \ne \set {0_V}$
where: 
:$0_V$ is the zero vector of $V$
:$I : V \to V$ is the identity mapping on $V$
:$\map \ker {A - \lambda I}$ denotes the kernel of $A - \lambda I$.
That is, $\lambda \in K$ is an '''eigenvalue of $A$''' {{iff}} the kernel of $A$ is non-trivial.
{{explain|Link to "non-trivial"}}
\end{definition}