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}