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Question. Is there a closed-form expression for the determinant of a $n \times n$ matrix $A$ with entries $$ A_{i,j} = \frac{1 - \delta_{i, j}}{z_i - z_j}, \qquad 1\leq i, j\leq n, $$ where $z_i$ ...

An $n\times n$ circulant matrix $\mathbf{X}_n$ has the form \begin{align} \mathbf{X}_n= \begin{bmatrix} x_1 & x_2 & \cdots & x_{n-1} & x_n \\ x_2 & x_3 & \cdots & x_n&...