Inequalities Involving the Numerical Radius

Charles R. Johnson, I. M. Spitkovsky, S. Gottlieb

Research output: Contribution to journalArticlepeer-review


For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open

Original languageEnglish (US)
Pages (from-to)13-24
Number of pages12
JournalLinear and Multilinear Algebra
Issue number1-3
StatePublished - Jun 1 1994

ASJC Scopus subject areas

  • Algebra and Number Theory


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