Abstract
Continuing Citation4, 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.
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Acknowledgements
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.