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Ordered vector space

In mathematics, an ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations.

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Overview

Definition

Positive cones and their equivalence to orderings

Intervals and the order bound dual

Examples

Properties

Spaces of linear maps

Special types of ordered vector spaces

Subspaces, quotients, and products

Bibliography

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Map overview Semantic statistics

Ordered vector space

Nodes94
Edges93
Triples46
Avg. degree1.98
Density0.021277
Components1

How this topic connects Entity context

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Ordered vector space

Top relations

related to Examples · 14
Ordered vector space → Archimedean, Euclidean, For, Furthermore, If, Its, Leftrightarrow B-A, Let Sym, Lexicographical, Riesz, Sym, The, The Loewner, This
related to Positive cones and their equivalence to orderings · 7
Ordered vector space → C-C, Given, If, PosCone, The, There, X/N
see also · 6
Ordered vector space → Algebraic, Construction, Group, Order, Partially, Topology
related to Intervals and the order bound dual · 5
Ordered vector space → An, From, If, In, The
related to Special types of ordered vector spaces · 5
Ordered vector space → Archimedean, Let, This, TVS, We
related to Spaces of linear maps · 4
Ordered vector space → C-C, If, In, More
related to Subspaces, quotients, and products · 2
Ordered vector space → Subspaces, Throughout
is a · 1
Ordered vector space → real vector space equipped with a partial order that is compatible with the vector space operations
related to Definition · 1
Ordered vector space → Given
related to Properties · 1
Ordered vector space → If

Important terminology Word statistics

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Important terminology

displaystyle vector space order leq cone ordered positive set mathbb preordered called geq proper cones spaces given convex text partial

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ordered vector spaceis areal vector space equipped with a partial order that is compatible with the vector space operations0.90text
Ordered vector spacerelated to DefinitionGiven0.60section
Ordered vector spacerelated to ExamplesIf0.60section
Ordered vector spacerelated to ExamplesThe0.60section
Ordered vector spacerelated to ExamplesFor0.60section
Ordered vector spacerelated to ExamplesEuclidean0.60section
Ordered vector spacerelated to ExamplesArchimedean0.60section
Ordered vector spacerelated to ExamplesLexicographical0.60section
Ordered vector spacerelated to ExamplesThis0.60section
Ordered vector spacerelated to ExamplesRiesz0.60section
Ordered vector spacerelated to ExamplesLet Sym0.60section
Ordered vector spacerelated to ExamplesSym0.60section

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    Min side: 3
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