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Cauchy–Schwarz functions and convex partitions in the ray space of a supertropical quadratic form
Linear and Multilinear Algebra ( IF 1.1 ) Pub Date : 2021-05-06 , DOI: 10.1080/03081087.2021.1919049
Zur Izhakian 1 , Manfred Knebusch 2
Affiliation  

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.



中文翻译:

超热带二次型射线空间中的 Cauchy–Schwarz 函数和凸分区

射线是超热带半环上模V上等价关系的类。他们提供了一个凸几何的版本,由“超热带三角学”支持并与拟线性兼容,其中 CS 比扮演柯西-施瓦茨不等式的角色。从 CS 比率出现的 CS 函数是一个有用的工具,有助于理解射线空间中各种拟线性恒星R一种(V). 特别地,这些功能引起了一个分区R一种(V)成凸集,从而得到更精细的凸分析,其中包括中值、最小值、峡谷和极坐标的概念。

更新日期:2021-05-06
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