Disc separation of the schur complement of diagonally dominant matrices and determinantal bounds

Abstract

We consider the Geršgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix Is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of diagonally dominant matrices. © 2006 Society for Indiustrial and Applied Mathematics.