  The self-adjoint matrix Sturm-Liouville operator on a finite interval with a
boundary condition in the general form is studied. We obtain asymptotic
formulas for the eigenvalues and the weight matrices of the considered
operator. These spectral characteristics play an important role in the inverse
spectral theory. Our technique is based on analysis of analytic functions and
on the contour integration in the complex plane of the spectral parameter. In
addition, we adapt the obtained asymptotic formulas to the Sturm-Liouville
operators on a star-shaped graph with two different types of matching
conditions.
