**Spectral Analysis of Block Jacobi Matrices with Singular Entries**

Three-diagonal block matrices (BM) are strictly connected with matrix-valued orthogonal polynomials (MOP).

Methods arising from the theory of those MOP gives answers to questions about spectrum of corresponding BM.

The case of singular coefficients in matrix-valued three-term recurrence formula such MOP satisfy will be treated.

The results will be applied to give another approach to the analysis of classic orthogonal polynomials satisfying three-term recurrence formula with periodic coefficients.

- M. J. Zygmunt: Matrix orthogonal polynomials and continued fractions,
*Linear Alg. Appl.*,**340**1-3 (2002), 155-168. - M. J. Zygmunt: Jacobi Block Matrices with Constant Matrix Terms,
*Oper. Theory: Adv. & Appl.*, 154 (2004), 233-238. - M. J. Zygmunt: Matrix orthogonal polynomials with respect to a non-symmetric matrix of measures, Opuscula Math.,
**36**3 (2016), 409-423.