# Definition:Eigenvector/Real Square Matrix

## Definition

Let $\mathbf A$ be a square matrix of order $n$ over $\R$.

Let $\lambda \in \R$ be an eigenvalue of $\mathbf A$.

A non-zero vector $\mathbf v \in \R^n$ is an eigenvector corresponding to $\lambda$ if and only if:

$\mathbf A \mathbf v = \lambda \mathbf v$