SIAM Journal on Matrix Analysis and Applications
Brauer theorem, Comparison matrix, Diagonally dominant matrix, Doubly diagonally dominant matrix, Gersgorin theorem, H-matrix, M-matrix, Schur complement, Separation
We consider the Gersgorin 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.
Liu, Jianzhou and Zhang, Fuzhen, "Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds" (2005). Mathematics Faculty Articles. 51.