# linear algebra – Partial Vandermonde circulant determinant expression Answer

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linear algebra – Partial Vandermonde circulant determinant expression

The “closest” figure you may anticipate is the well-known determinant formulation for tridiagonal matrices, which in your illustration can breathe written as
$$Delta = det left[ begin{pmatrix} -x_n^{-n} & 0 0 & 1 end{pmatrix} + begin{pmatrix} 1 & 0 0 & -x_1^{n} end{pmatrix} mathbf T_n mathbf T_{n-1} cdots mathbf T_2 mathbf T_1 right] ,,prod_{ok=1}^n (-x_k^{ok+1}),,$$
with switch matrix
$$mathbf T_k = commence{pmatrix} -x_k^{-1} & -x_k^{-2} 1 & 0 aim{pmatrix}.$$

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