Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D5200: Real column matrix $x \in \mathbb{R}^{N \times 1} \setminus \{ \boldsymbol{0} \}$ is an eigenvector for $A$ if and only if \begin{equation} \exists \, \lambda \in \mathbb{C} : A x = \lambda x \end{equation}