Dual spaces and bilinear forms in supertropical linear algebra

Zur Izhakian; Manfred Knebusch; Louis Rowen

doi:https://doi.org/10.1080/03081087.2012.676045

Dual spaces and bilinear forms in supertropical linear algebra

Zur Izhakian, Manfred Knebusch, Louis Rowen

Department of Mathematics

Bar-Ilan University

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

Abstract

Continuing 4, this article investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwartz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.

Original language	English
Pages (from-to)	865-883
Number of pages	19
Journal	Linear and Multilinear Algebra
Volume	60
Issue number	7
DOIs	https://doi.org/10.1080/03081087.2012.676045
State	Published - Jul 2012

Keywords

bilinear form
change of base semirings
d-base
dual base
linear algebra
s-base
tropical algebra
vector space

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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Cite this

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title = "Dual spaces and bilinear forms in supertropical linear algebra",

abstract = "Continuing 4, this article investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwartz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.",

keywords = "bilinear form, change of base semirings, d-base, dual base, linear algebra, s-base, tropical algebra, vector space",

author = "Zur Izhakian and Manfred Knebusch and Louis Rowen",

note = "Funding Information: The work of the first and third authors has been supported by the Israel Science Foundation, grant 448/09. The second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Mathematics Department of Bar-Ilan University, and the Emmy Noether Institute.",

year = "2012",

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doi = "https://doi.org/10.1080/03081087.2012.676045",

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TY - JOUR

T1 - Dual spaces and bilinear forms in supertropical linear algebra

AU - Izhakian, Zur

AU - Knebusch, Manfred

AU - Rowen, Louis

N1 - Funding Information: The work of the first and third authors has been supported by the Israel Science Foundation, grant 448/09. The second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Mathematics Department of Bar-Ilan University, and the Emmy Noether Institute.

PY - 2012/7

Y1 - 2012/7

N2 - Continuing 4, this article investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwartz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.

AB - Continuing 4, this article investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwartz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.

KW - bilinear form

KW - change of base semirings

KW - d-base

KW - dual base

KW - linear algebra

KW - s-base

KW - tropical algebra

KW - vector space

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U2 - https://doi.org/10.1080/03081087.2012.676045

DO - https://doi.org/10.1080/03081087.2012.676045

M3 - مقالة

SN - 0308-1087

VL - 60

SP - 865

EP - 883

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 7

ER -

Dual spaces and bilinear forms in supertropical linear algebra

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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