Izhakian, Zur and Knebusch, Manfred (2022) Cauchy-Schwarz functions and convex partitions in the ray space of a supertropical quadratic form. LINEAR & MULTILINEAR ALGEBRA, 70 (20). pp. 5502-5546. ISSN 0308-1087, 1563-5139
Full text not available from this repository. (Request a copy)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.
| Item Type: | Article |
|---|---|
| Uncontrolled 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 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Petra Gürster |
| Date Deposited: | 08 Feb 2023 11:12 |
| Last Modified: | 08 Feb 2023 11:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46853 |
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