Some basic spectral properties of complex tridiagonal matrices and the one-dimensional perturbations method.
Description:
In the talk we give some properties of the spectrum and the root subspaces of an arbitrary complex tridiagonal matrix. We also consider the related sequences of orthogonal polynomials and study their roots. Finally, we discuss some applications of the one-dimensional perturbations method developed (but not published) by Yu. S. Barkovsky to arbitrary complex tridiagonal matrices.