\begin{definition}[Definition:Eigenspace]
Let $K$ be a field.
Let $V$ be a vector space over $K$. 
Let $A : V \to V$ be a linear operator.
Let $I : V \to V$ be the identity mapping on $V$. 
Let $\lambda \in K$ be an eigenvalue of $A$. 
Let $\map \ker {A - \lambda I}$ be the kernel of $A - \lambda I$.
We say that $\map \ker {A - \lambda I}$ is the '''eigenspace''' corresponding to the eigenvalue $\lambda$.
\end{definition}