Extensions of the Hadamard determinant theorem
type: Item
instance of: scholarly article
title: Extensions of the Hadamard determinant theorem
zbMATH Open document ID: 0531.15003
DOI: 10.1007/BF02762889
author: Russell Merris
published in: Israel Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: Let \(A=(a_{ij})\) be an n by n positive definite Hermitian matrix, and put \(h(A)=a_{11}a_{22}...a_{nn}\). If G is a permutation group of degree n with identity e and \(\chi\) is an irreducible complex character of G, define \(d(A)=\Sigma \chi(\sigma)\Pi a_{t\sigma(t)}\) where \(t=1,...,n\) and the sum is over all permutations \(\sigma\) in G. The author extends Hadamard's determinant theorem by showing that \(h(A)\geq [d(A^{1/n})/\chi(e)]^ n\) for all A.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 3842055
zbMATH Keywords: Hadamard determinant theorem
zbMATH Keywords: generalized matrix function
zbMATH Keywords: positive definite Hermitian matrix
reviewed by: George Phillip Barker
MaRDI profile type: Publication
cites work: The permanent analogue of the Hadamard determinant theorem
cites work: The Hadamard Theorem for Permanents
cites work: Inequalities for the permanent function
cites work: A Convexity Proof of Hadamard's Inequality
cites work: Two problems involving Schur functions
cites work: Q3961594
cites work: Permanents
cites work: Mean Value and Limit Theorems for Generalized Matrix Functions
description: scientific article; zbMATH DE number 3842055