  The matrix Schr\"odinger equation is considered on the half line with the
general selfadjoint boundary condition at the origin described by two boundary
matrices satisfying certain appropriate conditions. It is assumed that the
matrix potential is integrable, is selfadjoint, and has a finite first moment.
The corresponding scattering data set is constructed, and such scattering data
sets are characterized by providing a set of necessary and sufficient
conditions assuring the existence and uniqueness of the correspondence between
the scattering data set and the input data set containing the potential and
boundary matrices. The work presented here provides a generalization of the
classical result by Agranovich and Marchenko from the Dirichlet boundary
condition to the general selfadjoint boundary condition. The theory presented
is illustrated with various explicit examples.
