We know that the determinant of a general tridiagonal n by n matrix is given by the n-th continuant, someone can see the section: Generalization in the following link: https://en.wikipedia.org/wiki/Continuant_(mathematics).
My question is if there is an explicit formula for the eigenvalues.
Thank you all.
Dear Hanifa, there exist explicit formulas for eigenvalues of several special tridiagonal matrices. See e.g. "Eigenvalues of several tridiagonal matrices" by W.C. Yueh and the references therein, or search on researchgate (or any other) database. I don't think there exists a general result.
If your matrix is Toeplitz of odd order, the eigenvalues are real and can be quite easily found.
Yes dear Viera. I see special cases and types like Toeplitz matrices and want to confirm that really there is no formula for general matrices.
Hanifa, to solve there are algorithms as it says by profesor Hernandez. The QR transformation was developed in the late 1950s by John G.F. Francis (England) and by Vera N. Kublanovskaya (USSR), working independently to calculate eigenvalues of a matrix
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