Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces
type: Item
instance of: scholarly article
title: Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces
zbMATH Open document ID: 1124.47003
author: Adrian Sandovici
author: H. S. V. de Snoo
author: Henrik Winkler
published in: Linear Algebra and its Applications
publication date: 2007-05-10T00:00:00Z
review text: The authors of the paper under review for a linear relation introduce and study the notions of ascent, descent, nullity, and defect. It is shown that the results of \textit{A.\,E.\thinspace Taylor} [Math.\ Ann.\ 163, 18--49 (1966; Zbl 0138.07602)] and \textit{M.\,A.\thinspace Kaashoek} [Math.\ Ann.\ 172, 105--115 (1967; Zbl 0152.33803)] for linear operators are also valid in the case of linear relations that do not have nontrivial singular chains. Examples are given that in the case when there are such chains, the corresponding results are not valid.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A06
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 5151580
zbMATH Keywords: linear relation
zbMATH Keywords: linear space
zbMATH Keywords: ascent
zbMATH Keywords: descent
zbMATH Keywords: nullity
zbMATH Keywords: defect
zbMATH Keywords: singular chain
zbMATH Keywords: complete reduction
MaRDI profile type: Publication
full work available at URL: j.laa.2007.01.024
OpenAlex ID: W2072678163
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DOI: 10.1016/J.LAA.2007.01.024
description: scientific article; zbMATH DE number 5151580