Singular M-matrices which may not have a nonnegative generalized inverse

Agrawal N. Sushama; K. Premakumari; K.C. Sivakumar

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 165-179, electronic only
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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Agrawal N. Sushama, K. Premakumari, and K.C. Sivakumar. "Singular M-matrices which may not have a nonnegative generalized inverse." Special Matrices 2.1 (2014): 165-179, electronic only. <http://eudml.org/doc/266709>.

@article{AgrawalN2014,
abstract = {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.},
author = {Agrawal N. Sushama, K. Premakumari, K.C. Sivakumar},
journal = {Special Matrices},
keywords = {Eventually nonnegative; Eventually positive; Perron-Frobenius property; Perron-Frobenius splitting; PFn; WPFn; eventually nonnegative; eventually positive},
language = {eng},
number = {1},
pages = {165-179, electronic only},
title = {Singular M-matrices which may not have a nonnegative generalized inverse},
url = {http://eudml.org/doc/266709},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Agrawal N. Sushama
AU - K. Premakumari
AU - K.C. Sivakumar
TI - Singular M-matrices which may not have a nonnegative generalized inverse
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 165
EP - 179, electronic only
AB - 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.
LA - eng
KW - Eventually nonnegative; Eventually positive; Perron-Frobenius property; Perron-Frobenius splitting; PFn; WPFn; eventually nonnegative; eventually positive
UR - http://eudml.org/doc/266709
ER -

References

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  12. [12] H.T. Le and J.J. McDonald, Inverses of M-type matrices created with irreducible eventually nonnegative matrices, Lin. Alg. Appl., 419 (2006), 668-674. Zbl1116.15008
  13. [13] D. Mishra and K.C. Sivakumar, On splitting of matrices and nonnegative generalized inverses, Oper. Matrices, 6 (2012), 85-95. [Crossref] Zbl1247.15003
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  15. [15] D. Noutsos, On Perron-Frobenius property of matrices having some negative entries, Lin. Alg. Appl., 412 (2006), 132–153. Zbl1087.15024
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