On matrices with different tropical and Kapranov ranks
type: Item
instance of: scholarly article
title: On matrices with different tropical and Kapranov ranks
zbMATH Open document ID: 1261.15006
DOI: 10.1134/S0001434612070310
published in: Mathematical Notes
publication date: 2013-02-22T00:00:00Z
review text: The author proves the folllowing result about the tropical rank of matrices: Let \(C\) be a \(5\times n\) real matrix with tropical rank at most 3. Then the Karpanov rank of \(C\), computed over a ground field of at least four elements, is at most 3. This is related to a question posed by \textit{M. Develin} et al. [Math. Sci. Res. Inst. Publ. 52, 213--242 (2005; Zbl 1095.15001)].
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 6138386
zbMATH Keywords: tropical semiring
zbMATH Keywords: tropical rank
zbMATH Keywords: Kapranov rank
zbMATH Keywords: tropical linear algebra
author: Ya. N. Shitov
MaRDI profile type: Publication
cites work: Linear independence over tropical semirings and beyond
cites work: Q4304869
cites work: Q5200628
cites work: Q4661963
cites work: RANK INEQUALITIES OVER SEMIRINGS
cites work: Q3181764
cites work: The \(4\times 4\) minors of a \(5\times n\) matrix are a tropical basis
Recommended article: On the Kapranov ranks of tropical matrices
Recommended article: Q5290261
Recommended article: The Tropical Rank of a Tropical Matrix
Recommended article: The ultimate rank of tropical matrices
Recommended article: Rank functions of tropical matrices
Recommended article: On tropical matrices of small factor rank
Recommended article: A separation between tropical matrix ranks
Recommended article: Three notions of tropical rank for symmetric matrices
Recommended article: Q4591290
Recommended article: Mixed subdivisions and ranks of tropical matrices
description: scientific article; zbMATH DE number 6138386