Abstract
We consider the class of doubly diagonally dominant matrices ( A = [a ij] ϵ C n, n, ∥a ii||a jj∥ ⩾ ∑ k ≠ i |a ik|∑ k ⩞ j|a jk|, i ≠ j ) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of doubly diagonally dominant matrices inherit this property. Moreover, we describe when a Schur complement of a strictly doubly diagonally dominant matrix is strictly diagonally dominant.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
