Further inequalities involving the Khatri-Rao product

被引：6

作者：

Yang, Zhongpeng ^{[2
]}

Liu, Shuangzhe ^{[1
]}

Trenkler, Goetz ^{[3
]}

机构：

[1] Univ Canberra, Fac Informat Sci & Engn, Canberra, ACT 2601, Australia

[2] Putian Univ, Dept Math, Putian 351100, Peoples R China

[3] Univ Dortmund, Dept Stat, D-44221 Dortmund, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 10期

关键词：

Hadamard product; Khatri-Rao product; Tracy-Singh product; Kronecker product; Schur complement; Matrix inequality; POSITIVE SEMIDEFINITE MATRICES; HADAMARD-PRODUCTS;

D O I：

10.1016/j.laa.2008.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Styan [G.RH. Styan, Hadamard products and multivariate statistical analysis, Linear Algebra Appl. 6 (1973) 217-240] established an inequality involving the Hadamard product using statistical reasoning in the context of multivariate analysis. In this paper, the inequality is extended to involve the Khatri-Rao product in the non-negative definite matrix case and in the non-singular Hermitian matrix case. The equality conditions for these extensions are given. Also established are counterpart inequalities in the positive definite matrix case. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：2696 / 2704

页数：9

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