# 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

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topAgrawal 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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