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A circulant matrix is a square matrix where each row has the same elements as the previous row, cyclically rotated right by one element. It is a specific kind of a square Toeplitz matrix.

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Partial Vandermonde circulant determinant expression

The "closest" form you can expect is the well known determinant formula for tridiagonal matrices, which in your case can be written as $$ \Delta = \det \left[ \begin{pmatrix} -x_n^{-n} & 0 \\ 0 & 1 …
Fred Hucht's user avatar
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