[…] As I have written previously, not many matrices have an explicit formula for eigenvalues. This is because eigenvalues are the roots of a high-order polynomial, and Galois theory proves that there is no general formula for high-order polynomials in terms of radicals (square roots, cube roots, etc). However, there are exceptions for classes of matrices that contain a lot of structure. For example, I have previously showed that there is an explicit formula for the eigenvalues of a tridiagonal Toeplitz matrix. …