Lower bounds for the numerical radius

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We show that if A = [aij]ni, j=1 is an n-by-n complex matrix and A′ = [a′i,j]ni, j=1, where (eqution found), then w(A)≥ w(A′), where w(·) denotes the numerical radius of a matrix. Moreover, if n is odd and a12,…,an−1,n,an1 are all nonzero, then w(A) = w(A′) if and only if A = A′. For an even n, under the same nonzero assumption, we have W(A) =W(A′) if and only if A = A′, where W(·) is the numerical range of a matrix.

Original languageEnglish
Pages (from-to)999-1014
Number of pages16
JournalOperators and Matrices
Issue number4
StatePublished - Dec 2017


  • Numerical radius
  • Numerical range


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