A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bt have ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative. In this article, we consider a generalization of a subclass of GM-matrices having a nonnegative core nilpotent decomposition and prove a characterization result for such matrices. Also, we study various notions of splitting of matrices from this new class and obtain sufficient conditions for their convergence.
@article{bwmeta1.element.doi-10_2478_spma-2014-0017,
author = {Agrawal N. Sushama and K. Premakumari and K.C. Sivakumar},
title = {Singular M-matrices which may not have a nonnegative generalized inverse},
journal = {Special Matrices},
volume = {2},
year = {2014},
zbl = {1307.15010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0017}
}
Agrawal N. Sushama; K. Premakumari; K.C. Sivakumar. Singular M-matrices which may not have a nonnegative generalized inverse. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0017/
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