Singular M-matrices which may not have a nonnegative generalized inverse
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 Bthave 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 nilpo...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-02-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.2478/spma-2014-0017 |
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doaj-68fd38e8f1e7493789651fb6d44b60c02021-10-02T19:16:02ZengDe GruyterSpecial Matrices2300-74512014-02-012110.2478/spma-2014-0017spma-2014-0017Singular M-matrices which may not have a nonnegative generalized inverseSushama Agrawal N.0Premakumari K.1Sivakumar K.C.2Ramanujan Institute of Advanced Study in Mathematics, University of Madras,Chennai,- 600005, IndiaRamanujan Institute of Advanced Study in Mathematics, University of Madras,Chennai,- 600005, IndiaDepartment of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, IndiaA 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 Bthave 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 decompositionand prove a characterization result for such matrices. Also, we study various notions of splitting of matricesfrom this new class and obtain sufficient conditions for their convergence.https://doi.org/10.2478/spma-2014-0017eventually nonnegative eventually positive perron-frobenius property perron-frobenius splittingpfn wpfn15a09 15b48 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sushama Agrawal N. Premakumari K. Sivakumar K.C. |
| spellingShingle |
Sushama Agrawal N. Premakumari K. Sivakumar K.C. Singular M-matrices which may not have a nonnegative generalized inverse Special Matrices eventually nonnegative eventually positive perron-frobenius property perron-frobenius splitting pfn wpfn 15a09 15b48 |
| author_facet |
Sushama Agrawal N. Premakumari K. Sivakumar K.C. |
| author_sort |
Sushama Agrawal N. |
| title |
Singular M-matrices which may not have a nonnegative generalized inverse |
| title_short |
Singular M-matrices which may not have a nonnegative generalized inverse |
| title_full |
Singular M-matrices which may not have a nonnegative generalized inverse |
| title_fullStr |
Singular M-matrices which may not have a nonnegative generalized inverse |
| title_full_unstemmed |
Singular M-matrices which may not have a nonnegative generalized inverse |
| title_sort |
singular m-matrices which may not have a nonnegative generalized inverse |
| publisher |
De Gruyter |
| series |
Special Matrices |
| issn |
2300-7451 |
| publishDate |
2014-02-01 |
| description |
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 Bthave 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 decompositionand prove a characterization result for such matrices. Also, we study various notions of splitting of matricesfrom this new class and obtain sufficient conditions for their convergence. |
| topic |
eventually nonnegative eventually positive perron-frobenius property perron-frobenius splitting pfn wpfn 15a09 15b48 |
| url |
https://doi.org/10.2478/spma-2014-0017 |
| work_keys_str_mv |
AT sushamaagrawaln singularmmatriceswhichmaynothaveanonnegativegeneralizedinverse AT premakumarik singularmmatriceswhichmaynothaveanonnegativegeneralizedinverse AT sivakumarkc singularmmatriceswhichmaynothaveanonnegativegeneralizedinverse |
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1716847515678015488 |