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}