Linear independence over tropical semirings and beyond

Details Linear independence over tropical semirings and beyond Linear independence over tropical semirings and beyond

2008-12-18

arxiv.org/abs/0812.3496v1

Proceedings of the International Conference on Tropical and Idempotent Mathematics, G.L. Litvinov and S.N. Sergeev Eds, volume

Mathematics

Commutative Algebra

Scientific paper

We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already received attention, we compare them with the ranks defined in terms of signed tropical determinants or arising from a notion of linear independence introduced by Gondran and Minoux. To do this, we revisit the symmetrization of the max-plus algebra, establishing properties of linear spaces, linear systems, and matrices over the symmetrized max-plus algebra. In parallel we develop some general technique to prove combinatorial and polynomial identities for matrices over semirings that we illustrate by a number of examples.

Affiliated with

Also associated with

No associations

Rating

Linear independence over tropical semirings and beyond 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 Linear independence over tropical semirings and beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear independence over tropical semirings and beyond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-173019