Ordering positive definite matrices

被引：0
|
作者：
Mostajeran C. [1 ]
Sepulchre R. [1 ]
机构：
[1] Department of Engineering, University of Cambridge, Cambridge
来源：
Information Geometry | 2018年 / 1卷 / 2期
基金：
欧洲研究理事会; 欧盟地平线“2020”; 英国工程与自然科学研究理事会;
关键词：
Differential positivity; Matrix means; Monotone flows; Monotone functions; Partial orders; Positive definite matrices;
D O I：
10.1007/s41884-018-0003-7
中图分类号：
学科分类号：
摘要：
We introduce new partial orders on the set Sn+ of positive definite matrices of dimension n derived from the affine-invariant geometry of Sn+. The orders are induced by affine-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous geometry of Sn+ defined by the natural transitive action of the general linear group GL(n). We then take a geometric approach to the study of monotone functions on Sn+ and establish a number of relevant results, including an extension of the well-known Löwner-Heinz theorem derived using differential positivity with respect to affine-invariant cone fields. © 2018, The Author(s).
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页码：287 / 313
页数：26
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