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eigenvalues of matrices or operators
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Eigenvalues of symmetric tridiagonal matrices with identical off diagonal elements
Is there a simple analytical solution to obtain eigenvalues (and eigenvectors) for this type of tridiagonal matrices ? … identical and the matrix is symmetric)
$$
\begin{pmatrix}
a_{1}-k & k & 0 & 0 \\\
k & a_{2}-2\cdot k & k & 0 \\\
0 & k & -a_{2}-2\cdot k & k \\\
0 & 0 & k & -a_{1}-k
\end{pmatrix}
$$
To obtain eigenvalues …