Tan's Epsilon-Determinant and Ranks of Matrices over Semirings

We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester i...

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Detalles Bibliográficos
Autores principales: Mohindru, Preeti, Pereira, Rajesh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2015
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897142/
https://www.ncbi.nlm.nih.gov/pubmed/27347506
http://dx.doi.org/10.1155/2015/242515
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author Mohindru, Preeti
Pereira, Rajesh
author_facet Mohindru, Preeti
Pereira, Rajesh
author_sort Mohindru, Preeti
collection PubMed
description We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester inequalities. We classify all bijective linear maps which preserve these ranks.
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spelling pubmed-48971422016-06-26 Tan's Epsilon-Determinant and Ranks of Matrices over Semirings Mohindru, Preeti Pereira, Rajesh Int Sch Res Notices Research Article We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester inequalities. We classify all bijective linear maps which preserve these ranks. Hindawi Publishing Corporation 2015-02-04 /pmc/articles/PMC4897142/ /pubmed/27347506 http://dx.doi.org/10.1155/2015/242515 Text en Copyright © 2015 P. Mohindru and R. Pereira. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Mohindru, Preeti
Pereira, Rajesh
Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title_full Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title_fullStr Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title_full_unstemmed Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title_short Tan's Epsilon-Determinant and Ranks of Matrices over Semirings
title_sort tan's epsilon-determinant and ranks of matrices over semirings
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897142/
https://www.ncbi.nlm.nih.gov/pubmed/27347506
http://dx.doi.org/10.1155/2015/242515
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AT pereirarajesh tansepsilondeterminantandranksofmatricesoversemirings

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