The eigenproblem of a tridiagonal 2-Toeplitz matrix

AbstractThe characteristic polynomial of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point Chebyshev recurrence relationship. This is an extension of the well-known result for a tridiagonal Toeplitz matrix. When the order of the matrix is odd, the eigenvalues are found explicitly in terms of the Chebyshev zeros. The eigenvectors are found in terms of the polynomials satisfying the three point recurrence relationship