Izhakian, Zur and Knebusch, Manfred (2022) Stratifications of the ray space of a tropical quadratic form by Cauchy-Schwartz functions. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 38. pp. 531-558. ISSN 1537-9582, 1081-3810
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Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of 'sup ertropical 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MODULES; Supertropical algebra; Supertropical modules; Bilinear forms; Quadratic forms; Quadratic pairs; Ray spaces; Convex sets; Quasilinear sets; Cauchy-Schwarz ratio; Cauchy-Schwarz functions; Stratifications |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Feb 2024 07:05 |
| Last Modified: | 15 Feb 2024 07:05 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57581 |
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