Affordable Access

Green's J-order and the rank of tropical matrices

Authors
  • Johnson, Marianne
  • Kambites, Mark
Type
Preprint
Publication Date
Jan 04, 2012
Submission Date
Feb 14, 2011
Identifiers
arXiv ID: 1102.2707
Source
arXiv
License
Yellow
External links

Abstract

We study Green's J-order and J-equivalence for the semigroup of all n-by-n matrices over the tropical semiring. We give an exact characterisation of the J-order, in terms of morphisms between tropical convex sets. We establish connections between the J-order, isometries of tropical convex sets, and various notions of rank for tropical matrices. We also study the relationship between the relations J and D; Izhakian and Margolis have observed that $D \neq J$ for the semigroup of all 3-by-3 matrices over the tropical semiring with $-\infty$, but in contrast, we show that $D = J$ for all full matrix semigroups over the finitary tropical semiring.

Report this publication

Statistics

Seen <100 times