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Alternating multilinear map

In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form) that is zero whenever any pair of its arguments is equal. This generalizes directly to a module over a commutative ring.

Alternatization, Properties & Example

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Alternatization

Symmetric mapBilinear mapCocycleCohomology groupLattice
6 related topics

Properties

RingAntisymmetricPermutation groupSignUnit
5 related topics

Example

Lie bracketDeterminant
2 related topics

Vector spaces

Linearly dependent
1 related topics

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Overview

Vector spaces

Example

Properties

Alternatization

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Map overview Semantic statistics

Alternating multilinear map

Nodes27
Edges26
Triples5
Avg. degree1.93
Density0.074074
Components1

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Alternating multilinear map

Top relations

related to Alternatization · 2
Alternating multilinear map → Given, Properties
related to Properties · 2
Alternating multilinear map → Every, If
is a · 1
Alternating multilinear map → multilinear map with all arguments belonging to the same vector space

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Important terminology

alternating map displaystyle multilinear alternatization bilinear form ring algebra mathematics vector ldots ed whenever arguments space isbn example leq vol

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Alternating multilinear mapis amultilinear map with all arguments belonging to the same vector space0.90text
Alternating multilinear maprelated to AlternatizationGiven0.60section
Alternating multilinear maprelated to AlternatizationProperties0.60section
Alternating multilinear maprelated to PropertiesIf0.60section
Alternating multilinear maprelated to PropertiesEvery0.60section

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