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.
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}