Orthogonal Tropical Linear Prevarieties

摘要

We study the operation A～⊥ of tropical orthogonalization, applied to a subset A of a vector space (R∪{∞})～n, and iterations of this operation. Main results include a criterion and an algorithm, deciding whether a tropical linear prevariety is a tropical linear variety formulated in terms of a duality between A～⊥ and A～(⊥⊥). We give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.