Quasi-positive definite operators and matrices
type: Item
instance of: scholarly article
title: Quasi-positive definite operators and matrices
zbMATH Open document ID: 0654.15022
DOI: 10.1016/0024-3795(88)90130-9
author: Dipa Choudhury
author: Roger A. Horn
author: Stephen J. Pierce
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let F be the real or complex field, let \(V_ 1,V_ 2,...,V_ m\) be finite dimensional inner product spaces over F, and let W be their tensor product. Relative to the natural inner product induced on W by the inner products on the \(V_ i\), a Hermitian linear operator T on W is said to be quasi-positive definite (semidefinite) if the Hermitian form \(<Tw,w>\) is positive (nonnegative) for all nonzero decomposition tensors w in W. Properties of such operators are studied with emphasis given to their negative inertia and the relation between their largest and smallest eigenvalues. The authors observe that a better understanding of quasi- positive semidefinite operators may lead to resolution of some conjectured inequalities for generalized matrix functions.
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4067121
zbMATH Keywords: inner product spaces
zbMATH Keywords: tensor product
zbMATH Keywords: Hermitian linear operator
zbMATH Keywords: quasi- positive definite
zbMATH Keywords: Hermitian form
zbMATH Keywords: negative inertia
zbMATH Keywords: largest and smallest eigenvalues
zbMATH Keywords: inequalities
zbMATH Keywords: matrix functions
reviewed by: Peter Gibson
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90130-9
OpenAlex ID: W2024191900
cites work: On Quadratic and Bilinear Forms in Function Theory
cites work: Unitary and Orthogonal Transformations on Matrices
cites work: Matrix Analysis
cites work: The Hadamard Theorem for Permanents
cites work: Q4128900
cites work: Linear maps and tensor rank
description: scientific article; zbMATH DE number 4067121