The structure of linear relations in Euclidean spaces

Adrian Sandovici; Hendrik de Snoo; Henrik Winkler; Adrian Sandovici

doi:10.1016/j.laa.2004.10.008

The structure of linear relations in Euclidean spaces

Adrian Sandovici, Hendrik de Snoo, Henrik Winkler, Adrian Sandovici

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Abstract

The structure of a linear relation (inultivalued operator) in a Euclidean space is completely determined. A linear relation can be written as a direct sum of three relations of different classes, which are Jordan relations, completely singular relations and multishifts. All three classes of relations are characterized in terms of the spectrum and their chain structure, which leads to a generalization of the classical Jordan canonical form. (C) 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	141-169
Number of pages	29
Journal	Linear Algebra and Its Applications
Volume	397
DOIs	https://doi.org/10.1016/j.laa.2004.10.008
Publication status	Published - 1-Mar-2005

Keywords

linear relation
linear space
Euclidean space
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keywords = "linear relation, linear space, Euclidean space, OPERATORS",

author = "Adrian Sandovici and {de Snoo}, Hendrik and Henrik Winkler and Adrian Sandovici",

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AU - de Snoo, Hendrik

AU - Winkler, Henrik

AU - Sandovici, Adrian

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

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Y1 - 2005/3/1

N2 - The structure of a linear relation (inultivalued operator) in a Euclidean space is completely determined. A linear relation can be written as a direct sum of three relations of different classes, which are Jordan relations, completely singular relations and multishifts. All three classes of relations are characterized in terms of the spectrum and their chain structure, which leads to a generalization of the classical Jordan canonical form. (C) 2004 Elsevier Inc. All rights reserved.

AB - The structure of a linear relation (inultivalued operator) in a Euclidean space is completely determined. A linear relation can be written as a direct sum of three relations of different classes, which are Jordan relations, completely singular relations and multishifts. All three classes of relations are characterized in terms of the spectrum and their chain structure, which leads to a generalization of the classical Jordan canonical form. (C) 2004 Elsevier Inc. All rights reserved.

KW - linear relation

KW - linear space

KW - Euclidean space

KW - OPERATORS

U2 - 10.1016/j.laa.2004.10.008

DO - 10.1016/j.laa.2004.10.008

M3 - Article

SN - 0024-3795

VL - 397

SP - 141

EP - 169

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The structure of linear relations in Euclidean spaces

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