Let $A \in \mathbb{R}^{N \times N}$ be a D4571: Real matrix.
A D1207: Complex number $\lambda \in \mathbb{C}$ is a complex eigenvalue for $A$ if and only if
\begin{equation}
\exists \, x \in \mathbb{R}^{N \times 1} \setminus \{ \boldsymbol{0} \} :
A x = \lambda x
\end{equation}