The eigenproblem of a tridiagonal 2-Toeplitz matrix (Q1319980): Difference between revisions

A solution of the eigenproblem for a tridiagonal 2-Toeplitz matrix is presented. It is shown that the characteristic polynomial for the case \(r = 2\) of a generalized \(r\)-Toeplitz matrix possesses similar properties as the Chebyshev polynomial of the first kind. When the order of the matrix is odd then the eigenvalues can be found explicitly. The case of matrices with even order is not handled straightforwardly by means of Chebyshev zeroes. A formula for explicit calculation of eigenvectors of 2-Toeplitz matrices is presented.