# Definition:Eigenvalue/Real Square Matrix

## Definition

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

Let $\lambda \in \R$.

$\lambda$ is an eigenvalue of $A$ if and only if there exists a non-zero vector $\mathbf v \in \R^n$ such that:

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