Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
Let $I_N \in \mathbb{C}^{N \times N}$ be a D5699: Complex identity matrix.

Then \begin{equation} \exists \, \lambda_1, \, \ldots, \, \lambda_N \in \mathbb{C} : \forall \, z \in \mathbb{C} : \text{Det}(z I_N - A) = \prod^N_{n = 1} (z - \lambda_n) \end{equation}