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) | $A$ is a D5949: Lower triangular complex matrix |
| (ii) | \begin{equation} A = \begin{bmatrix} A_{1, 1} & 0 & \cdots & 0 \\ A_{2, 1} & A_{2, 2} & \vdots & 0 \\ \vdots & \cdots & \ddots & \vdots \\ A_{N, 1} & A_{N, 2} & \cdots & A_{N, N} \end{bmatrix} \end{equation} |
Then
\begin{equation}
\text{Det}(z I_N - A)
= \prod_{n = 1}^N (z - A_{n, n})
\end{equation}