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20 votes
6 answers
42k views

Eigenvalues of symmetric tridiagonal matrices

Suppose I have the symmetric tridiagonal matrix: $$ \begin{pmatrix} a & b_{1} & 0 & ... & 0 \\\ b_{1} & a & b_{2} & \ddots & \vdots \\\ 0 & b_{2} & a & \...
FlamingWilderbeest's user avatar
15 votes
4 answers
7k views

Eigenvectors and eigenvalues of a tridiagonal Toeplitz matrix

Is it possible to analytically evaluate the eigenvectors and eigenvalues of the following $n \times n$ tridiagonal matrix $$ \mathcal{T}^{a}_n(p,q) = \begin{pmatrix} 0 & q & 0 & 0 &...
user22127's user avatar
  • 153
7 votes
1 answer
3k views

How can I calculate eigenvalues of a tridiagonal matrix? [closed]

Are there special methods to get exact eigenvalues of a tridiagonal matrix?
Abdelhak Hafdallah's user avatar