ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5514 on D5717: Complex matrix determinant
Determinant of a complex identity matrix
Formulation 0
Let $I_N \in \mathbb{C}^{N \times N}$ be a D5699: Complex identity matrix.
Then \begin{equation} \text{Det} I_N = 1 \end{equation}
Proofs
Proof 0
Let $I_N \in \mathbb{C}^{N \times N}$ be a D5699: Complex identity matrix.
This result is a particular case of R5070: Determinant of a diagonal complex matrix with constant diagonal. $\square$