Matrix determinant with complex coefficients

Question

Let $n$ a positive integer, define $A=left(e^{frac{2i(k-1)(l-1)pi}{n}}right)_{1 leq k,l leq n} $ , evaluate $det(A)$.

Velobos · Answer

Actually, the determinant of this Matrix is a Vandermonde determinant.
You have : $A = mathcal{V}(w,w^2,...,w^{n-1})$ where $w=e^{frac{2ipi}{n}}$, and you know the formula for the Vandermonde determinant.

Matrix determinant with complex coefficients

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