The new estimations of diagonally dominant degree and eigenvalues distributions for the schur complements of block diagonally dominant matrices and determinantal bounds

In this paper, some new estimations of diagonally dominant degree on the Schur complement of I(II)-block diagonally dominant matrices are obtained by applying the properties of Schur complement and some inequality techniques, which improve some existing ones. Further, as an application, we present some new distribution theorems for eigenvalues of the Schur complement and some new upper and lower bounds for the determinant of I(II)-block diagonally dominant matrices. These results are proved to be sharper than some known ones. Finally, numerical examples are also presented to confirm the theoretical results studied in this paper.