ThmDex – An index of mathematical definitions, results, and conjectures.
Determinant of a triangular complex matrix
Formulation 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) $A$ is a D5947: Triangular complex matrix
Then \begin{equation} \text{Det} A = \prod_{n = 1}^N A_{n, n} \end{equation}
Also known as
Determinant of a triangular complex square matrix equals the product of the diagonal elements, Only the diagonal contributes to the determinant of a triangular complex matrix
Subresults
▶ R5560: Characteristic polynomial for a triangular complex matrix
▶ R5074: Determinant of a lower triangular complex matrix
▶ R5073: Determinant of an upper triangular complex matrix