Numerical radius of Hadamard product of matrices

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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).

Original languageEnglish
Pages (from-to)292-308
Number of pages17
JournalLinear Algebra and Its Applications
StatePublished - 1 Sep 2016


  • Hadamrad product
  • Normal matrix
  • Numerical radius
  • Positive semidefinite matrix


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