The dominant degree and disc theorem for the Schur complement of matrix

The theory of Schur complement plays an important role in many fields such as control theory and computational mathematics. In this paper, we obtain some estimates for the diagonally, γ-diagonally and product γ-diagonally dominant degree on the Schur complement of matrices, which improve some relative results. As application we present some bounds for the eigenvalues of Schur complement by the entries of the original matrix instead of those of the Schur complement. Particularly, we obtain that the eigenvalues of the Schur complements are located in the Gerschgorin Circles of the original matrices under certain conditions.