Symmetric tridiagonal Toeplitz matrix
= Symmetric tridiagonal Toeplitz matrix
An $m\times m$ symmetric tridiagonal Toeplitz matrix has one constant diagonal $\alpha$ and equal constant subdiagonal and superdiagonal $\beta$. Its eigenvectors are the <discrete sine transform> vectors $q^{(k)}_j=\sin(jk\pi/(m+1))$, with eigenvalues $\alpha+2\beta\cos(k\pi/(m+1))$.