  In this paper we introduce the concept of matrix-valued $q$-rational
functions. In comparison to the classic case we give different
characterizations with principal emphasise on realizations and discuss
algebraic manipulations. We also study the concept of Schur multipliers and
complete Nevanlinna Pick kernels in this context and provide first applications
in terms of an interpolation problem using Schur multipliers and complete
Nevanlinna Pick kernels.
