Matrix results on the Khatri-Rao and Tracy-Singh products

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Abstract

We establish a connection between the Khatri-Rao and Tracy-Singh products introduced by Khatri and Rao (C.G. Khatri, C.R. Rao, Sankhya 30 (1968) 167-180) and Tracy and Singh (D.S. Tracy, R.P. Singh, Statistica Neerlandica 26 (1972) 143-157), respectively, and present further results including matrix equalities and inequalities involving the two products. Also, we give two statistical applications.

Original languageEnglish
Pages (from-to)267-277
Number of pages11
JournalLinear Algebra and Its Applications
Volume289
Issue number1
DOIs
Publication statusPublished - 1 Mar 1999
Externally publishedYes

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title = "Matrix results on the Khatri-Rao and Tracy-Singh products",
abstract = "We establish a connection between the Khatri-Rao and Tracy-Singh products introduced by Khatri and Rao (C.G. Khatri, C.R. Rao, Sankhya 30 (1968) 167-180) and Tracy and Singh (D.S. Tracy, R.P. Singh, Statistica Neerlandica 26 (1972) 143-157), respectively, and present further results including matrix equalities and inequalities involving the two products. Also, we give two statistical applications.",
keywords = "Albert's theorem, Hadamard product, Khatri-Rao product, Kronecker product, Matrix inequality, Moore-penrose inverse, Tracy-Singh product",
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Matrix results on the Khatri-Rao and Tracy-Singh products. / Liu, Shuangzhe.

In: Linear Algebra and Its Applications, Vol. 289, No. 1, 01.03.1999, p. 267-277.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Matrix results on the Khatri-Rao and Tracy-Singh products

AU - Liu, Shuangzhe

PY - 1999/3/1

Y1 - 1999/3/1

N2 - We establish a connection between the Khatri-Rao and Tracy-Singh products introduced by Khatri and Rao (C.G. Khatri, C.R. Rao, Sankhya 30 (1968) 167-180) and Tracy and Singh (D.S. Tracy, R.P. Singh, Statistica Neerlandica 26 (1972) 143-157), respectively, and present further results including matrix equalities and inequalities involving the two products. Also, we give two statistical applications.

AB - We establish a connection between the Khatri-Rao and Tracy-Singh products introduced by Khatri and Rao (C.G. Khatri, C.R. Rao, Sankhya 30 (1968) 167-180) and Tracy and Singh (D.S. Tracy, R.P. Singh, Statistica Neerlandica 26 (1972) 143-157), respectively, and present further results including matrix equalities and inequalities involving the two products. Also, we give two statistical applications.

KW - Albert's theorem

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(98)10209-4

DO - 10.1016/S0024-3795(98)10209-4

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VL - 289

SP - 267

EP - 277

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

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ER -