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

פרסום מחקרי: פרסום בכתב עת › מאמר › ביקורת עמיתים

51 ציטוטים ‏(Scopus)

תקציר

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.

שפה מקורית	אנגלית
עמודים (מ-עד)	3912-3927
מספר עמודים	16
כתב עת	Communications in Algebra
כרך	37
מספר גיליון	11
מזהי עצם דיגיטלי (DOIs)	https://doi.org/10.1080/00927870902828793
סטטוס פרסום	פורסם - נוב׳ 2009
פורסם באופן חיצוני	כן

גישה למסמך

10.1080/00927870902828793

קבצים וקישורים אחרים

Link to publication in Scopus

פורמט ציטוט ביבליוגרפי

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title = "The tropical rank of a tropical matrix",

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.",

year = "2009",

month = nov,

doi = "10.1080/00927870902828793",

language = "אנגלית",

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AU - Izhakian, Zur

AU - Rowen, Louis

N1 - 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.

PY - 2009/11

Y1 - 2009/11

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.

AB - 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.

KW - Extended tropical semiring

KW - Linear algebra

KW - Linear dependence

KW - Matrix algebra

KW - Pseudo invertibility

KW - Rank of matrices

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U2 - 10.1080/00927870902828793

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AN - SCOPUS:74949089679

SN - 0092-7872

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

The tropical rank of a tropical matrix

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