Partial orderings, preorderings, and the polar decomposition of matrices
type: Item
instance of: scholarly article
title: Partial orderings, preorderings, and the polar decomposition of matrices
zbMATH Open document ID: 0932.15014
DOI: 10.1016/S0024-3795(98)10108-8
author: Jürgen Gross
author: Jan Hauke
author: Augustyn Markiewicz
published in: Linear Algebra and its Applications
publication date: 2000-03-02T00:00:00Z
review text: The starting point is the well known polar decomposition of a complex \(m\times n\)-matrix. It can be made unique by imposing additional conditions on the factors. Each partial order on one of the domains of this decomposition gives rise to a preordering on \({\mathbb C}^{m\times n}\). If we are given a partial order on both domains, then the intersection of the corresponding preorderings is a partial ordering on \({\mathbb C}^{m\times n}\). The domains of the unique polar decomposition are now endowed, respectively, with one of three partial orderings (Löwner, star, and rank subtractivity), and the corresponding preorderings and partial orderings are investigated.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 1331298
zbMATH Keywords: polar decomposition
zbMATH Keywords: partial ordering
zbMATH Keywords: preordering
zbMATH Keywords: partial isometry
zbMATH Keywords: Löwner partial ordering
zbMATH Keywords: star partial ordering
zbMATH Keywords: rank subtractivity partial ordering
reviewed by: Hans Havlicek
MaRDI profile type: Publication
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full work available at URL: s0024-3795(98)10108-8
OpenAlex ID: W2065968604
Wikidata QID: Q127014984
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description: scientific article; zbMATH DE number 1331298