Tropical Arithmetic and Tropical Matrix Algebra

• Published in 2005
• Added on 2012-02-03

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.

Links

• http://arxiv.org/abs/math/0505458
• http://arxiv.org/pdf/math/0505458v3

Other information

BibTeX entry

@article{Izhakian2005,
	key = {Izhakian2005},
	type = {article},
	title = {Tropical Arithmetic and Tropical Matrix Algebra},
	author = {Izhakian, Zur},
	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.},
	comment = {},
	date_added = {2012-02-03},
	date_published = {2005-05-01},
	urls = {http://arxiv.org/abs/math/0505458,http://arxiv.org/pdf/math/0505458v3},
	collections = {Unusual arithmetic},
	archivePrefix = {arXiv},
	arxivId = {math/0505458},
	eprint = {math/0505458},
	journal = {ReCALL},
	keywords = {Algebraic Geometry,Combinatorics},
	month = {may},
	pages = 17,
	primaryClass = {math.AG},
	url = {http://arxiv.org/abs/math/0505458 http://arxiv.org/pdf/math/0505458v3},
	year = 2005,
	urldate = {2012-02-03}
}