Numerical radius of Hadamard product of matrices

Hwa Long Gau; Pei Yuan Wu

doi:10.1016/j.laa.2016.04.013

Numerical radius of Hadamard product of matrices

Hwa Long Gau, Pei Yuan Wu

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研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

7 引文斯高帕斯（Scopus）

摘要

It is known that the numerical radius of the Hadamard product A ○ B of two n-by-n matrices A and B is related to those of A and B by (a) w(A ○ B) ≤ 2w(A)w(B), (b) w(A ○ B) ≤ w(A)w(B) if one of A and B is normal, and (c) w(A ○ B) ≤ (max_ia_ii)w(B) if A = [a_ij]_i,j=1ⁿ is positive semidefinite. In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining (Equation Presented).

原文	???core.languages.en_GB???
頁（從 - 到）	292-308
頁數	17
期刊	Linear Algebra and Its Applications
卷	504
DOIs	https://doi.org/10.1016/j.laa.2016.04.013
出版狀態	已出版 - 1 9月 2016

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10.1016/j.laa.2016.04.013

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AU - Gau, Hwa Long

AU - Wu, Pei Yuan

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N2 - It is known that the numerical radius of the Hadamard product A ○ B of two n-by-n matrices A and B is related to those of A and B by (a) w(A ○ B) ≤ 2w(A)w(B), (b) w(A ○ B) ≤ w(A)w(B) if one of A and B is normal, and (c) w(A ○ B) ≤ (maxiaii)w(B) if A = [aij]i,j=1n is positive semidefinite. In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining (Equation Presented).

AB - It is known that the numerical radius of the Hadamard product A ○ B of two n-by-n matrices A and B is related to those of A and B by (a) w(A ○ B) ≤ 2w(A)w(B), (b) w(A ○ B) ≤ w(A)w(B) if one of A and B is normal, and (c) w(A ○ B) ≤ (maxiaii)w(B) if A = [aij]i,j=1n is positive semidefinite. In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining (Equation Presented).

KW - Hadamrad product

KW - Normal matrix

KW - Numerical radius

KW - Positive semidefinite matrix

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U2 - 10.1016/j.laa.2016.04.013

DO - 10.1016/j.laa.2016.04.013

M3 - 期刊論文

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EP - 308

JO - Linear Algebra and Its Applications

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ER -

Numerical radius of Hadamard product of matrices

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