On the Weyl matrix balls corresponding to the matricial Carathéodory problem in both nondegenerate and degenerate cases

The main goal of the paper is to determine the Weyl matrix balls associated with an arbitrary matricial Carathéodory problem. For the special case of a nondegenerate matricial Carathéodory problem the corresponding Weyl matrix balls were computed by I.V. Kovalishina [Ko] and alternatively by the first and the second authors in [FK1, Parts IV and V].status: publishe