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I am studying Toeplitz matrices. I have to find out the eigenvalues of the following Toeplitz matrix:

$\begin{bmatrix} 2 & -8 & -24 \\ 3 & 2 & -8 \\ 1 & 3 & 2 \end{bmatrix}$

Are there any different procedures to find out eigenvalues of Toeplitz matrices?

Can't I use the general method of finding eigenvalues for them too? I need help with this. I need a MATLAB code also.

I am studying the following paper - Generalized Inverses of Certain Toeplitz Matrices.

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    For tri-diagonal Toeplitz matrices there is an explicit formula. See p. 6 of this paper http://arxiv.org/abs/1110.66202012-07-05

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The following MATLAB code will find the eigenvalues of the matrix in your question:

A = toeplitz([2 3 1], [2 -8 -24]); eigvalues = eig(A); 
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Of course you can use the same methods you would use for a non-Toeplitz matrix, and for something as small as this one there's no reason not to do so. You would only need a special algorithm for a matrix too large to handle by the usual methods. On the other hand, eigenvalues of large Toeplitz matrices can be numerically unstable, see e.g. Eigenvalues and Pseudo Eigenvalues of Toeplitz Matrices (Lothar Reichel, Lloyd N. Trefethen).