The tropical rank of a tropical matrix

Zur Izhakian; Louis Rowen

doi:10.1080/00927870902828793

The tropical rank of a tropical matrix

Zur Izhakian
, Louis Rowen

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

Abstract

In this article, we develop further the theory of matrices over the extended tropical semiring. We introduce the notion of tropical linear dependence, enabling us to define matrix rank in a sense that coincides with the notions of tropical nonsingularity and invertibility.

Original language	English
Pages (from-to)	3912-3927
Number of pages	16
Journal	Communications in Algebra
Volume	37
Issue number	11
DOIs	https://doi.org/10.1080/00927870902828793
State	Published - Nov 2009
Externally published	Yes

Keywords

Extended tropical semiring
Linear algebra
Linear dependence
Matrix algebra
Pseudo invertibility
Rank of matrices

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10.1080/00927870902828793

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abstract = "In this article, we develop further the theory of matrices over the extended tropical semiring. We introduce the notion of tropical linear dependence, enabling us to define matrix rank in a sense that coincides with the notions of tropical nonsingularity and invertibility.",

keywords = "Extended tropical semiring, Linear algebra, Linear dependence, Matrix algebra, Pseudo invertibility, Rank of matrices",

author = "Zur Izhakian and Louis Rowen",

note = "Funding Information: The first author would like to express his sincere thanks to Prof. E. Shustin for his invaluable help. I am deeply grateful to him for our fertile discussions. The author has been supported by The German–Israeli Foundation for Research and Development by Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.",

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N2 - In this article, we develop further the theory of matrices over the extended tropical semiring. We introduce the notion of tropical linear dependence, enabling us to define matrix rank in a sense that coincides with the notions of tropical nonsingularity and invertibility.

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KW - Extended tropical semiring

KW - Linear algebra

KW - Linear dependence

KW - Matrix algebra

KW - Pseudo invertibility

KW - Rank of matrices

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JO - Communications in Algebra

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The tropical rank of a tropical matrix

Abstract

Keywords

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