Computer-aided study of a problem in Hermitian matrix theory
type: Item
instance of: scholarly article
title: Computer-aided study of a problem in Hermitian matrix theory
zbMATH Open document ID: 0716.15012
DOI: 10.1016/S0747-7171(08)80009-0
author: Man Kam Kwong
author: Mary Beth Dever
published in: Journal of Symbolic Computation
publication date: 1990-01-01T00:00:00Z
review text: Let A be an \(n\times n\) positive definite Hermitian matrix and let B be an \(n\times n\) nonnegative semidefinite Hermitian matrix. For \(n\geq 3\), there is a smallest real number \(t_ n>2\) such that if \(-2<t\leq t_ n\) then the solution X to the equation \(A^ 2X+XA^ 2+tAXA=B\) is nonnegative semidefinite Hermitian. The authors describe their use of REDUCE and MAPLE in showing that \(t_ 4=4\) and in obtaining bounds for \(t_ n\) when \(5\leq n\leq 8\).
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 4179561
zbMATH Keywords: symbolic computation
zbMATH Keywords: matrix equation
zbMATH Keywords: positive definite Hermitian matrix
zbMATH Keywords: REDUCE
zbMATH Keywords: MAPLE
zbMATH Keywords: bounds
reviewed by: Peter Gibson
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Hermitian Matrix Inequalities and a Conjecture
cites work: On the definiteness of the solutions of certain matrix equations
description: scientific article; zbMATH DE number 4179561