Maximal elements under the three partial orders
type: Item
instance of: scholarly article
title: Maximal elements under the three partial orders
zbMATH Open document ID: 0767.15017
DOI: 10.1016/0024-3795(92)90301-P
author: R. E. Hartwig
author: Raphael Loewy
published in: Linear Algebra and its Applications
publication date: 1993-01-16T00:00:00Z
review text: Three useful partial orders on a class of \(n\times n\) complex matrices are studied: The star order, minus order and the Loewner or positive semidefinite order. The authors characterize the maximal elements for each of these, when they exist, in a number of classes including the projections, the idempotents, the unitary matrices, and the contractions. In the class of nilpotent matrices they characterize the maximal elements of the star and minus orders but obtain only partial results describing the maximal elements for the positive semidefinite order.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 47L07
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 95475
zbMATH Keywords: partial orders
zbMATH Keywords: star order
zbMATH Keywords: minus order
zbMATH Keywords: positive semidefinite order
zbMATH Keywords: maximal elements
zbMATH Keywords: projections
zbMATH Keywords: idempotents
zbMATH Keywords: unitary matrices
zbMATH Keywords: contractions
zbMATH Keywords: nilpotent matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 95475