A generalization of bergstrom's inequality and some applications

Sze Fong Yau, Yoram Bresler

Research output: Contribution to journalArticle

Abstract

Bergstrom's inequality is generalized. Using the new inequality, several interesting results concerning Hadamard product of matrices are proved. More specifically, let P,Q ε{lunate} CN×N such that P>0 and Q≥0, Qii>0. Then we prove the following tight inequalities: (a) Qii[(P⊙Q)-1]ii≤ (P-1ii; (b) Qii{[Re(P⊙Q)]-1}ii ≤ max {[Re(φPφ*)]-1}ii; (c) det(P⊙Q)≥ (detP)πNi=1 Qii; (d) det Re(P⊙ Q) ≥ min det[Re(φPφ*)]πNi=1 Qii, where in (b) and (d) maximization and minimization are over all unitary diagonal matrices φε{lunate}CN×N.

Original languageEnglish (US)
Pages (from-to)135-151
Number of pages17
JournalLinear Algebra and Its Applications
Volume161
Issue numberC
DOIs
StatePublished - Jan 15 1992

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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