Dual spaces and bilinear forms in supertropical linear algebra
Zur Izhakian, Manfred Knebusch, Louis Halle Rowen · Linear and Multilinear Algebra · 2012
Continuing 4 Izhakian, Z, Knebusch, M and Rowen, L. Supertropical linear algebra, preprint 2010. Available at arXiv:1008.0025 [Google Scholar], 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.