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) | $c \in \mathbb{C}$ is a D1207: Complex number |
(ii) | \begin{equation} A = \begin{bmatrix} c & 0 & \cdots & 0 \\ 0 & c & \vdots & \vdots \\ \vdots & \cdots & \ddots & \vdots \\ 0 & \cdots & \cdots & c \end{bmatrix} \end{equation} |
Then
\begin{equation}
\text{Det}(z I_N - A)
= (z - c)^N
\end{equation}