Spectral properties of tridiagonal matrices with two-periodic main diagonal via orthogonal polynomials

Given a matrix with two-periodic main diagonal, we describe properties of its spectrum and eigenvectors consuming its relation to orthogonal polynomials. We provide exact formulas for eigenvalues and (generalised) eigenvectors provided the spectral properties of the matriz with the same sub- and superdiagonals and zero man diagonal are known.
The talk is based on a joint work with Alexander Dyachenko (KIAM RAS).