Dual Spaces and Bilinear Forms in Supertropical Linear Algebra

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.