The Hadamard core of the totally nonnegative matrices

被引：11

作者：

Crans, AS

Fallat, SM ^{[1
]}

Johnson, CR

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92507 USA

[3] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2001年 / 328卷 / 1-3期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

totally nonnegative matrices; Hadamard product; Hadamard core; zero-nonzero patterns; Oppenheim's inequality;

D O I：

10.1016/S0024-3795(00)00337-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An m-by-n matrix A is called totally nonnegative if every minor of A is nonnegative. The Hadamard product of two matrices is simply their entry-wise product, This paper introduces the subclass of totally nonnegative matrices whose Hadamard product with any totally nonnegative matrix is again totally nonnegative, Many properties concerning this class are discussed including: a complete characterization for min{m, n} < 4; a characterization of the zero-non-zero patterns for which all totally nonnegative matrices lie in this class; and connections to Oppenheim's inequality, <(c)> 2001 Elsevier Science Inc, All rights reserved.

引用

页码：203 / 222

页数：20

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