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Can you please help me find the distribution of eigenvalues of a Toeplitz matrix $\mathbf{K}$ that is constructed as follows: $$\mathbf{K}=\left[ \begin{array}{cccc} 1 & \rho & \ldots & \, \, \rho^{N-1} \\ \rho & 1 & \ldots & \, \,\rho^{N-2}\\ \vdots & \vdots & \ddots & \vdots \\ \rho^{N-1} & \rho^{N-2} & \ldots & 1 \\ \end{array} \right].$$ where $0 \leq \rho < 1$.

Thanks a lot in advance,

Farzad

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    what do you mean by 'distribution' ? Are all the elements numbers (as opposed to random variables) ? Do you need this in analytical form or is a numerical solution sufficient ?2011-08-15
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    @ Andre, Thanks a lot for your comment, you are right. Then, there is any analytical equation to evaluate eigenvalues?2011-08-15
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    Because this question is purely about the eigenvalues of these matrices, it is more suited for posting on math.SE.2011-08-15

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