ThmDex – An index of mathematical definitions, results, and conjectures.
Determinant of reflected complex matrix
Formulation 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
Then \begin{equation} \text{Det}(- A) = (-1)^N \text{Det} A \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
This result is a particular case of R5068: Determinant of a scaled complex matrix. $\square$