[Math] Eigenvalues and eigenvectors of a Toeplitz matrix

Question

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 MATLAB code also. I am studying the following paper

• R. E. Cline, R. J. Plemmons, G. Worm, Generalized inverses of certain Toeplitz matrices, Linear Algebra and its Applications, Volume 8, Issue 1, February 1974.

Answer 1

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);