Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
A D5689: Complex column matrix $z \in \mathbb{C}^{N \times 1} \setminus \{ \boldsymbol{0} \}$ is an eigenvector for $A$ if and only if \begin{equation} \exists \, \lambda \in \mathbb{C} : A z = \lambda z \end{equation}