TY - JOUR

T1 - Cauchy–Schwarz functions and convex partitions in the ray space of a supertropical quadratic form

AU - Izhakian, Zur

AU - Knebusch, Manfred

N1 - Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - 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 (Formula presented.). In particular, these functions induce a partition of (Formula presented.) into convex sets, and thereby a finer convex analysis which includes the notions of median, minima, glens, and polars.

AB - 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 (Formula presented.). In particular, these functions induce a partition of (Formula presented.) into convex sets, and thereby a finer convex analysis which includes the notions of median, minima, glens, and polars.

KW - Cauchy–Schwarz functions

KW - Cauchy–Schwarz ratio

KW - QL-stars

KW - Supertropical algebra

KW - bilinear forms

KW - convex sets

KW - quadratic forms

KW - quadratic pairs

KW - quasilinear sets

KW - ray spaces

KW - supertropical modules

UR - http://www.scopus.com/inward/record.url?scp=85105456289&partnerID=8YFLogxK

U2 - 10.1080/03081087.2021.1919049

DO - 10.1080/03081087.2021.1919049

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AN - SCOPUS:85105456289

SN - 0308-1087

VL - 70

SP - 5502

EP - 5546

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 20

ER -