Several inequalities involving Khatri-Rao products of positive semidefinite matrices

被引：21

作者：

Liu, SZ ^{[1
]}

机构：

[1] Australian Natl Univ, Sch Math Sci, Canberra, ACT 0200, Australia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 354卷 / 1-3期

关键词：

Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; MoorePenrose inverse; matrix inequality;

D O I：

10.1016/S0024-3795(02)00338-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. Based on the connection between the Khatri-Rao and Tracy-Singh products, we establish new inequalities involving Khatri-Rao products of positive semidefinite matrices. The results lead to inequalities involving Hadamard products, as a special case. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：175 / 186

页数：12

共 50 条

[21] Rank inequalities for positive semidefinite matrices
Lundquist, M
Barrett, W
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 248 : 91 - 100
[22] PRODUCTS OF POSITIVE SEMIDEFINITE MATRICES
WU, PY
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 111 : 53 - 61
[23] PROBLEM OF EQUALITIES IN EIGENVALUE INEQUALITIES FOR PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES
Xi Boyan(Inner Mongolia Teachers College for Nationalities
[J]. Numerical Mathematics(Theory,Methods and Applications), 2000, (S1) : 95 - 97
[24] Norm Inequalities for Positive Semidefinite Matrices
ZOU Limin1
2. College of Mathematics and Statistics
[J]. Wuhan University Journal of Natural Sciences, 2012, 17 (05) : 454 - 456
[25] Generalized Schur Complements Involving the Kronecker Products of Positive Semidefinite Matrices
Lou, L. H.
[J]. MATHEMATICAL NOTES, 2020, 107 (1-2) : 129 - 139
[26] Singular value inequalities involving convex and concave functions of positive semidefinite matrices
Fadi Alrimawi
Omar Hirzallah
Fuad Kittaneh
[J]. Annals of Functional Analysis, 2020, 11 : 1257 - 1273
[27] Generalized Schur Complements Involving the Kronecker Products of Positive Semidefinite Matrices
L. H. Lou
[J]. Mathematical Notes, 2020, 107 : 129 - 139
[28] Singular value inequalities involving convex and concave functions of positive semidefinite matrices
Alrimawi, Fadi
Hirzallah, Omar
Kittaneh, Fuad
[J]. ANNALS OF FUNCTIONAL ANALYSIS, 2020, 11 (04) : 1257 - 1273
[29] Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition
Bharadwaj, Vivek
Malik, Osman Asif
Murray, Riley
Grigori, Laura
Buluc, Aydin
Demmel, James
[J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 36 (NEURIPS 2023), 2023,
[30] Matrix results on the Khatri-Rao and Tracy-Singh products, (vol 289, pg 267, 1999)
Liu, SZ
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 320 (1-3) : 212 - 212

← 1 2 3 4 5 →