Please help support CiteULike by taking part in our marketing survey.
CiteULike is a free online bibliography manager. Register and you can start organising your references online.

Linear independence over tropical semirings and beyond Export

(18 Dec 2008)

Citation Format

[Posts]

View FullText article


X Reviews [Write a review of this article]

X Find related articles from these CiteULike users

X Find related articles with these CiteULike tags

X Posting History

X Abstract

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.


X BibTeX record

X RIS record