  In this paper we study the Nevanlinna-Pick matrix interpolation problem in
the Carath\'eodory class with infinite data (both in the nondegenerate and
degenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operator
approach to obtain an analytic description of all solutions of the problem.
Simple necessary and sufficient conditions for the determinacy of the problem
are given.
