Tropical Arithmetic and Tropical Matrix Algebra
Algebraic Geometry
2010-08-02 v3 Combinatorics
Abstract
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical matrix is invertible if and only if it is regular.
Cite
@article{arxiv.math/0505458,
title = {Tropical Arithmetic and Tropical Matrix Algebra},
author = {Zur Izhakian},
journal= {arXiv preprint arXiv:math/0505458},
year = {2010}
}
Comments
17 pages, 2 figures