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
Descripción
Sumario: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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