A note on spectral properties of a Dirac system with matrix coefficient

In this paper, we find a polynomialtype Jost solution of a selfadjoint matrixvalued discrete Dirac system. Then we investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation theorem, we prove that matrixvalued discrete Dirac system has continuous spectrum filling the segment [-2, 2]. Finally, we examine the properties of the eigenvalues of this Dirac system and we prove that it has a finite number of simple real eigenvalues.