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
收藏
页码：2696 / 2704
页数：9
相关论文
共 50 条
  • [1] INEQUALITIES INVOLVING THE KHATRI-RAO PRODUCT OF MATRICES
    Micic, Jadranka
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2009, 3 (04): : 617 - 630
  • [2] Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices
    Zeyad Abdel Aziz Al Zhour
    Adem Kilicman
    [J]. Journal of Inequalities and Applications, 2006
  • [3] Inequalities involving Khatri-Rao products of hermitian matrices
    Yang Z.-P.
    Zhang X.
    Cao C.-G.
    [J]. Journal of Applied Mathematics and Computing, 2002, 9 (1) : 125 - 133
  • [4] Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices
    Al Zhour, Zeyad Abdel Aziz
    Kilicman, Adem
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1)
  • [5] Several inequalities involving Khatri-Rao products of positive semidefinite matrices
    Liu, SZ
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 354 : 175 - 186
  • [6] Determinantal inequalities for block Hadamard product and Khatri-Rao product of positive definite matrices
    Dong, Sheng
    Wang, Qingwen
    Hou, Lei
    [J]. AIMS MATHEMATICS, 2022, 7 (06): : 9648 - 9655
  • [7] On the Restricted Isometry of the Columnwise Khatri-Rao Product
    Khanna, Saurabh
    Murthy, Chandra R.
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2018, 66 (05) : 1170 - 1183
  • [8] Jensen's Type Inequalities Involving Tracy-Singh Products, Khatri-Rao Products, Tracy-Singh Sums and Khatri-Rao Sums
    Ploymukda, Arnon
    Chansangiam, Pattrawut
    [J]. THAI JOURNAL OF MATHEMATICS, 2020, : 61 - 80
  • [9] Squeezed Random Khatri-Rao Product Codes
    Ji, Ruowan
    Pradhan, Asit Kumar
    Heidarzadeh, Anoosheh
    Narayanan, Krishna R.
    [J]. 2021 IEEE INFORMATION THEORY WORKSHOP (ITW), 2021,
  • [10] The Khatri-Rao Product of Block Diagonally Dominant Matrices
    Xie, Qingming
    Hu, Linchao
    Liu, Jianzhou
    [J]. ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 346 - 349
12345