The tropical analogue of polar cones

Details The tropical analogue of polar cones The tropical analogue of polar cones

2008-05-23

arxiv.org/abs/0805.3688v2

Linear Algebra and its Applications, Volume 431, pages 608-625, 2009

Mathematics

Metric Geometry

21 pages, 3 figures, example added, figures improved, notation changed

Scientific paper

10.1016/j.laa.2009.03.012

We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the inequalities satisfied by the elements of a tropical convex cone. We derive this characterization from a new separation theorem. We also establish variants of these results concerning systems of linear equalities.

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