Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
Let $z \in \mathbb{C}$ be a D1207: Complex number.
| (i) | $c_1, \ldots, c_N \in \mathbb{C}$ are each a D1207: Complex number |
| (ii) | \begin{equation} A = \begin{bmatrix} c_1 & 0 & \cdots & 0 \\ 0 & c_2 & \vdots & \vdots \\ \vdots & \cdots & \ddots & \vdots \\ 0 & \cdots & \cdots & c_N \end{bmatrix} \end{equation} |
Then
\begin{equation}
\text{Det}(z I_N - A)
= \prod_{n = 1}^N (z - c_n)
\end{equation}