Gaussian variables, polynomials and permanents
type: Item
instance of: scholarly article
title: Gaussian variables, polynomials and permanents
zbMATH Open document ID: 0934.15036
DOI: 10.1016/S0024-3795(98)10125-8
published in: Linear Algebra and its Applications
publication date: 1999-11-28T00:00:00Z
review text: It is proved that for \(n\) given unit vectors \(({\mathbf a}_{j})^{n}_{j=1}\) in a complex Hilbert space there exists such a unit vector \(\mathbf x\) that the inequality \( |\langle {\mathbf x}, {\mathbf a}_{1} \rangle\dots\langle {\mathbf x},{\mathbf a}_{n} \rangle |\geq n^{-n/2}\) holds. This result is derived on the basis of similar bounds for norms in real Hilbert and Banach spaces and on the basis of properties of complex Gaussian variables and permanents of a positive semidefinite Hermitian \(n \times n\) matrix.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 46C05
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 1371027
zbMATH Keywords: Gaussian variables
zbMATH Keywords: polynomials
zbMATH Keywords: permanents
zbMATH Keywords: complex Hilbert space
author: Juan Arias de Reyna
MaRDI profile type: Publication
cites work: The Pythagorean Theorem in Certain Symmetry Classes of Tensors
cites work: Lower Bounds for Norms of Products of Polynomials
cites work: Q4184984
cites work: Q5520710
cites work: Simple proof of a theorem on permanents
cites work: Q3715635
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description: scientific article; zbMATH DE number 1371027