Definition:Eigenvector/Linear Operator

Definition
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 $A$.

We say that a non-zero vector $v \in V$ is an eigenvector corresponding to $\lambda$ :


 * $v \in \map \ker {A - \lambda I}$

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, :


 * $A v = \lambda v$

Also see

 * Definition:Eigenvalue of Linear Operator