Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\)
type: Item
instance of: scholarly article
title: Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\)
zbMATH Open document ID: 0645.15007
DOI: 10.1016/0024-3795(88)90321-7
author: Thomas H. Pate
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let M be an \(n\times n\) positive semidefinite Hermitian matrix and \(W=(w_{ij})\) either a \(2\times 2\) real matrix such that \(w_{11}w_{22}\geq 0\) and \(w_{12}w_{21}\geq 0\) or a \(2\times 2\) Hermitian matrix such that \(w_{11}w_{22}\geq 0\). The author proves that per (W\(\otimes M)\geq (per W)^ n(per M)^ 2\). The cases of equality are discussed.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 4051802
zbMATH Keywords: permanent
zbMATH Keywords: positive semidefinite Hermitian matrix
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90321-7
OpenAlex ID: W2038871929
cites work: An inequality involving permanents of certain direct products
cites work: Permanent of the direct product of matrices
cites work: Permanents of Direct Products
cites work: Norm of symmetric product compared with norm of tensor product
cites work: Q4059065
cites work: Q4106341
description: scientific article; zbMATH DE number 4051802