A geometric estimate on the norm of product of functionals

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The open problem of determining the exact value of the n-th linear polarization constant cn of Rn has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of sup ∥y∥=1|〈x1, y〉⋯〈x n, y〉|, where x1,...,xn are unit vectors in ℝn. The new estimate is given in terms of the eigenvalues of the Gram matrix [〈xi, xj〉] and improves upon earlier estimates of this kind. However, the intriguing conjecture cn = nn/2 remains open.

Original languageEnglish
Pages (from-to)304-310
Number of pages7
JournalLinear Algebra and Its Applications
Volume405
Issue number1-3
DOIs
Publication statusPublished - Aug 1 2005

Fingerprint

Polarization
Gram Matrix
Norm
Unit vector
Estimate
Open Problems
Lower bound
Eigenvalue

Keywords

  • Gram matrices
  • Linear polarization constants
  • Polynomials over normed spaces
  • Product of functionals

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

A geometric estimate on the norm of product of functionals. / Matolcsi, M.

In: Linear Algebra and Its Applications, Vol. 405, No. 1-3, 01.08.2005, p. 304-310.

Research output: Contribution to journalArticle

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