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Convex cone

In linear algebra, a cone—sometimes called a linear cone to distinguish it from other sorts of cones—is a subset of a real vector space that is closed under positive scalar multiplication; that is, C {\displaystyle C} is a cone if x ∈ C {\displaystyle x\in C} implies s x ∈ C {\displaystyle sx\in C} for every positive scalar s {\displaystyle s} . This is…

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Overview

Definition

Examples

Special examples

Dual cone

Constructions

Partial order defined by a convex cone

Advanced semantic analysis

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Map overview Semantic statistics

Convex cone

Nodes62
Edges61
Triples39
Avg. degree1.97
Density0.032258
Components1

How this topic connects Entity context

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Convex cone

Top relations

related to Examples · 5
Convex cone → Each, For, In, The, These
related to Face of a convex cone · 5
Convex cone → For, Let, Suppose, The, Then
related to Partial order defined by a convex cone · 5
Convex cone → Examples, If, Loewner, Such, Sums
related to Affine convex cones · 4
Convex cone → An, For, However, Technically
related to Convex cone · 4
Convex cone → Also, Because, Some, This
is a · 3
Convex cone → cone that is also closed under addition, set resulting from applying an affine transformation to a convex cone, special case of a linear cone as defined above.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations
related to Blunt, pointed, flat, salient, and proper cones · 3
Convex cone → According, Blunt, Some
related to Competing definitions · 3
Convex cone → Some, The, Therefore
related to Dual cone · 3
Convex cone → Consider, Let, The
related to Half-spaces · 3
Convex cone → Farkas, Half-spaces, Moreover

Important terminology Word statistics

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Important terminology

cone displaystyle convex vector space set cones subset linear closed positive polyhedral also defined definition called vectors every salient mathbb

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Convex coneis acone that is also closed under addition0.90text
Convex coneis aspecial case of a linear cone as defined above.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations0.90text
Convex coneis aset resulting from applying an affine transformation to a convex cone0.90text
Convex conerelated to Affine convex conesAn0.60section
Convex conerelated to Affine convex conesTechnically0.60section
Convex conerelated to Affine convex conesFor0.60section
Convex conerelated to Affine convex conesHowever0.60section
Convex conerelated to Blunt, pointed, flat, salient, and proper conesAccording0.60section
Convex conerelated to Blunt, pointed, flat, salient, and proper conesSome0.60section
Convex conerelated to Blunt, pointed, flat, salient, and proper conesBlunt0.60section
Convex conerelated to Competing definitionsSome0.60section
Convex conerelated to Competing definitionsThe0.60section

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    Min side: 3
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