The Disc Theorem for the Schur Complement of Two Class Submatrices with γ-Diagonally Dominant Properties

摘要

The distribution for eigenvalues of Schur complement of matrices plays an important role in many mathematical problems.In this paper,we firstly present some criteria for H-matrix.Then as application,for two class matrices whose submatrices are γ-diagonally dominant and product γ-diagonally dominant,we show that the eigenvalues of the Schur complement are located in the Ger~gorin discs and the Ostrowski discs of the original matrices under certain conditions.