Inverse problem solution and spectral data characterization for the matrix Sturm–Liouville operator with singular potential

The self-adjoint matrix Sturm–Liouville operator on a finite interval with singular potential of class $$W_2^{-1}$$ and the general boundary conditions is studied. This generalizes operators geometrical graphs. We investigate inverse problem that consists in recovering considered from spectral data (eigenvalues weight matrices). reduced to linear equation suitable Banach space, constructive algorithm for solution developed. Moreover, we obtain characterization studied operator. In addition, main results are applied graph arbitrary structure.