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Find the determinant of the AR(1) matrix given by: $$R = \begin{pmatrix} 1 & \rho & \cdots & \rho^{d-1}\\ \rho & 1 & \cdots & \rho^{d-2}\\ \vdots & \vdots & \ddots & \vdots\\ \rho^{d-1} & \rho^{d-2} & \cdots & 1 \end{pmatrix}$$

This is a common question but I want a simpler method of computation that is without using results of determinants of tridiagonal matrices. Please help!

Rodrigo de Azevedo
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  • Could you add more entries to the matrix? I'm not sure I understand the pattern – overfull hbox Oct 25 '19 at 03:44
  • If I'm getting the construction of the matrix right, then it is a particular case of Theorem 1 in my answer https://math.stackexchange.com/questions/1383741/is-this-determinant-always-non-negative/1384516#1384516 (with all $p_i$ equal to $\rho$). – darij grinberg Oct 25 '19 at 03:46
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    Somewhat related: https://math.stackexchange.com/q/2815525/339790 – Rodrigo de Azevedo Oct 25 '19 at 05:49
  • The solution of that duplicated candidate uses tridiagonal matrices, which the OP said wasn't wanted. Voting to keep open. –  Oct 26 '19 at 07:48

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