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> $\alpha+2\beta\cos(k\pi/(m+1))$.