Tropical Arithmetic and Tropical Matrix Algebra

Details Tropical Arithmetic and Tropical Matrix Algebra Tropical Arithmetic and Tropical Matrix Algebra

2005-05-22

arxiv.org/abs/math/0505458v3

Communication in Algebra, 37(4):1445 - 1468 , 2009

Mathematics

Algebraic Geometry

17 pages, 2 figures

Scientific paper

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.

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