Abstract
We study the operation \(A^\perp \) of tropical orthogonalization, applied to a subset A of a vector space \(({\mathbb R}\cup \{ \infty \})^n\), 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 \(A^\perp \) and \(A^{\perp \perp }\). We give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.
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