Inequalities for mixed Schur functions
type: Item
instance of: scholarly article
title: Inequalities for mixed Schur functions
zbMATH Open document ID: 0602.15013
DOI: 10.1016/0024-3795(86)90271-5
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: Let \(A^ k=(a^ k_{ij})\) be a set of n positive semidefinite matrices each of order n. Let \(\alpha\) : \(S_ n\to {\mathbb{C}}\) where \(S_ n\) is the symmetric group of degree n. The ''mixed Schur function'' is the function of \(A^ 1,...,A^ n\) given by \(\sum \alpha (\sigma) \overline{\alpha (\tau)}\prod^{n}_{i=1}a^ i_{\sigma (i)\tau (i)}\) where \(\sigma\) and \(\tau\) run independently over \(S_ n\). The author obtains an inequality for this function and explores some of the consequences of this inequality.
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 3970947
zbMATH Keywords: positive semidefinite matrices
zbMATH Keywords: symmetric group
zbMATH Keywords: mixed Schur function
author: R. B. Bapat
reviewed by: George Phillip Barker
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90271-5
OpenAlex ID: W2043115841
cites work: Q5771003
cites work: An extremal property of the permanent and the determinant
cites work: Group Characters and the Structure of Groups
cites work: On two classical results of I. Schur
cites work: Some inequalities for combinatorial matrix functions
cites work: Inequalities for Matrix Functions of Combinatorial Interest
cites work: Q4348659
cites work: Theory of permanents 1978–1981
cites work: Constructing symmetric nonnegative matrices
description: scientific article; zbMATH DE number 3970947