Cauchy-Schwarz functions and convex partitions in the ray space of a supertropical quadratic form

Zur Izhakian, Manfred Knebusch

Research output: Working paper

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Abstract

Rays are classes of an equivalence relation on a module V over a supertropical semiring. They provide a version of convex geometry, supported by a "supertropical trigonometry" and compatible with quasilinearity, in which the CS-ratio takes the role of the Cauchy-Schwarz inequality. CS-functions which emerge from the CS-ratio are a useful tool that helps to understand the variety of quasilinear stars in the ray space Ray(V). In particular, these functions induce a partition of Ray(V) into convex sets, and thereby a finer convex analysis which includes the notions of median, minima, glens, and polars.
Original languageEnglish
PublisherArXiv
Number of pages39
Publication statusSubmitted - 30 Sep 2019

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Keywords

  • Supertropical algebra
  • supertropical modules
  • bilinear forms
  • quadratic forms
  • quadratic pairs
  • ray spaces
  • convex sets
  • quasilinear sets
  • Cauchy-Schwarz ratio
  • Cauchy-Schwarz functions
  • QL-stars

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