Dual Spaces and Bilinear Forms in Supertropical Linear Algebra

TL;DR

This paper advances supertropical linear algebra by exploring dual bases, bilinear forms, and classical theorems like Gram-Schmidt and Cauchy-Schwarz, adapting them to the supertropical setting.

Contribution

It introduces supertropical versions of quadratic forms, dual bases, and classical theorems, enriching the theoretical framework of supertropical vector spaces.

Findings

Established supertropical Gram-Schmidt process

Derived supertropical Cauchy-Schwarz inequality

Linked quadratic forms to symmetric bilinear forms in supertropical context

Abstract

Continuing [5], this paper 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-Schwarz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.