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

Department of Mathematics

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

7 Scopus citations

Abstract

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).

Original language	English
Pages (from-to)	292-308
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	504
DOIs	https://doi.org/10.1016/j.laa.2016.04.013
State	Published - 1 Sep 2016

Keywords

Hadamrad product
Normal matrix
Numerical radius
Positive semidefinite matrix

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AU - Gau, Hwa Long

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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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DO - 10.1016/j.laa.2016.04.013

M3 - 期刊論文

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SN - 0024-3795

VL - 504

SP - 292

EP - 308

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Numerical radius of Hadamard product of matrices

Abstract

Keywords

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