Abstract
Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of ‘supertropical trigonometry’ and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy–Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called CS-functions. These functions partite the ray space Ray(V) into convex sets and establish the main tool for analyzing varieties of quasilinear stars in Ray(V). They provide stratifications of Ray(V) and, therefore, a finer convex analysis that helps better understand geometric properties.
Original language | English |
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Pages (from-to) | 531-558 |
Number of pages | 28 |
Journal | Electronic Journal of Linear Algebra |
Volume | 38 |
DOIs | |
State | Published - 2022 |
Keywords
- Bilinear forms
- Cauchy–Schwarz functions
- Cauchy–Schwarz ratio
- Convex sets
- Quadratic forms
- Quadratic pairs
- Quasilinear sets
- Ray spaces
- Stratifications
- Supertropical algebra
- Supertropical modules
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory