The Disc Theorem for the Schur Complement of Two Class Submatrices with γ-Diagonally Dominant Properties. Issue 1 (20th February 2017) - Li, Guangqi; Liu, Jianzhou; Zhang, Juan
Abstract: 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 Geršgorin discs and the Ostrowski discs of the original matrices under certain conditions.