Eigenvector

Definition: Eigenvector

Let $A\in F^{n\times n}$ be a square matrix.

A non-zero vector $\vec{v}\in F^n$ is an eigenvector of a $A$ if there is some $\lambda \in F$ such that

$$A\vec{v}=\lambda \vec{v}$$

In this case, we also say that $\vec{v}$ belongs to the eigenvalue $\lambda$.

NOTE

An eigenvector can only belong to a single eigenvalue.