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

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

2011-02-14

arxiv.org/abs/1102.2707v2

Mathematics

Rings and Algebras

21 pages, exposition improved

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Green's J-order and the rank of tropical matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Green's J-order and the rank of tropical matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Green's J-order and the rank of tropical matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215287