\begin{definition}[Definition:Eigenvalue/Real Square Matrix]
Let $\mathbf A$ be a square matrix of order $n$ over $\R$. 
Let $\lambda \in \R$. 
$\lambda$ is an '''eigenvalue''' of $A$ if there exists a non-zero vector $\mathbf v \in \R^n$ such that: 
:$\mathbf A \mathbf v = \lambda \mathbf v$
\end{definition}