Schur Complements Of ?-?-block Diagonally Dominant Matrices And Their Appications

The Schur complement of matrices is one of the important topics in matrix theory and its application,and it is also an important method to study the properties of matrices.In this thesis,we reference the introduction process from diagonally dominant matrices to ?-diagonally dominant matrix and ?-block diagonally dominant matrix to ?-?block diagonally dominant matrix,and generalize the concepts of ?-block diagonally dominant matrices to ?-?-block diagonally dominant matrices and product ??-block diagonally dominant matrices,prove that the Schur complements of ?-?block diagonally dominant matrices(product?-?-block diagonally dominant matrices)are ?-?-block diagonally dominant matrices(product?-?-block diagonally dominant matrices),and give the diagonally dominant degree of Schur complement and the distribution of eigenvalues of these two kinds of matrices.