Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices

Fuzhen Zhang, Roger A. Horn

Research output: Contribution to journalArticlepeer-review

Abstract

X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius

Original languageAmerican English
Pages (from-to)90-94
Number of pages5
JournalElectronic Journal of Linear Algebra
Volume20
DOIs
StatePublished - Jan 1 2010

ASJC Scopus Subject Areas

  • Algebra and Number Theory

Keywords

  • Hadamard product
  • Kronecker product
  • Matrix inequality
  • Nonnegative matrix
  • Positive definite matrix
  • Positive semidefinite matrix
  • Spectral radius

Disciplines

  • Mathematics

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