Majorization in Euclidean geometry and beyond

被引：2
|
作者：
Fiedler, Miroslav [1 ]
机构：
[1] Acad Sci Czech Republic, Inst Comp Sci, Prague 18207 8, Czech Republic
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 466卷
关键词：
Majorization; Doubly stochastic matrix; Euclidean simplex; Star; Regular simplex; Volume of a simplex;
D O I：
10.1016/j.laa.2014.10.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We relate the well known notion of majorization to the behavior of a pair of simplices in a Euclidean n-space. We obtain a geometrical meaning for the determinant of the involved doubly stochastic matrix. Independently, a basic theorem about volumes of simplices contained one in another, even if of different dimensions, is proved. Some related geometric questions are also presented. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：233 / 240
页数：8
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