Dual spaces and bilinear forms in supertropical linear algebra

被引：5

作者：

Izhakian, Zur ^{[1
]}

Knebusch, Manfred ^{[2
]}

Rowen, Louis ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

[2] Univ Regensburg, Dept Math, Regensburg, Germany

来源：

LINEAR & MULTILINEAR ALGEBRA | 2012年 / 60卷 / 07期

关键词：

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

D O I：

10.1080/03081087.2012.676045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：865 / 883

页数：19

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