Several inequalities involving Khatri–Rao products of positive semidefinite matrices

Shuangzhe Liu

doi:10.1016/S0024-3795(02)00338-5

Several inequalities involving Khatri–Rao products of positive semidefinite matrices

Shuangzhe Liu

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	175-186
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	354
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(02)00338-5
Publication status	Published - 15 Oct 2002
Externally published	Yes

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title = "Several inequalities involving Khatri–Rao products of positive semidefinite matrices",

abstract = "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.",

keywords = "Hadamard product, Khatri–Rao product, Kronecker product, Matrix inequality, Moore–Penrose inverse, Tracy–Singh product",

author = "Shuangzhe Liu",

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AU - Liu, Shuangzhe

PY - 2002/10/15

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N2 - 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.

AB - 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.

KW - Hadamard product

KW - Khatri–Rao product

KW - Kronecker product

KW - Matrix inequality

KW - Moore–Penrose inverse

KW - Tracy–Singh product

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U2 - 10.1016/S0024-3795(02)00338-5

DO - 10.1016/S0024-3795(02)00338-5

M3 - Article

AN - SCOPUS:85014085914

SN - 0024-3795

VL - 354

SP - 175

EP - 186

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Several inequalities involving Khatri–Rao products of positive semidefinite matrices

Abstract

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