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

Zur Izhakian* (Corresponding Author), Manfred Knebusch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 that 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
Number of pages45
JournalLinear and Multilinear Algebra
Early online date6 May 2021
DOIs
Publication statusE-pub ahead of print - 6 May 2021

Keywords

  • Algebra and Number Theory
  • 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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