Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples

被引：24
|
作者：
Fallat, Shaun [1 ]
Johnson, Charles R. [2 ]
Sokal, Alan D. [3 ,4 ]
机构：
[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada
[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[3] NYU, Dept Phys, 4 Washington Pl, New York, NY 10003 USA
[4] UCL, Dept Math, London WC1E 6BT, England
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 520卷
基金：
英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;
关键词：
Totally positive matrix; Totally nonnegative matrix; Hankel matrix; Stieltjes moment problem; Hadamard product; Hadamard power; Hadamard critical exponent; MATRICES;
D O I：
10.1016/j.laa.2017.01.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that, for Hankel matrices, total nonnegativity (resp. total positivity) of order r is preserved by sum, Hadamard product, and Hadamard power with real exponent t >= r-2. We give examples to show that our results are sharp relative to matrix size and structure (general, symmetric or Hankel). Some of these examples also resolve the Hadamard critical exponent problem for totally positive and totally nonnegative matrices. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：242 / 259
页数：18
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