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Multivector

In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as decomposable k-vectors or k-blades) of the form

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Overview

Exterior product

Area and volume

Grassmann coordinates

Clifford product

Geometric algebra

Applications

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Multivector

Nodes56
Edges55
Triples44
Avg. degree1.96
Density0.035714
Components1

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Multivector

Top relations

related to Grassmann coordinates · 9
Multivector → For, Grassmann, In, P2, Pn, Points, R3, Rn, Thus
related to Multivectors on projective 3-space P3 · 7
Multivector → Let, Notice, P3, R4, The, Therefore, Three-dimensional
related to Geometric algebra · 6
Multivector → According, Clifford Algebra, David Hestenes, Geometric Calculus, Multivectors, The
related to Multivectors on the projective plane P2 · 6
Multivector → Notice, P2, Points, R3, The, Therefore
related to Exterior product · 5
Multivector → Alternating, Associative, Linear, The, This
related to Clifford product · 4
Multivector → Clifford, Clifford's, Hamilton's, The Clifford
related to Multivectors in R2 · 3
Multivector → Let, Properties, R2
related to Multivectors in R3 · 3
Multivector → In, More, R3
is a · 1
Multivector → dimension of the vector space V.Linearity in either input together with the alternating property implies linearity in the other input

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Important terminology

space vector vectors product algebra exterior called plane points linear projective k-vector coordinates also element multivectors components bivector homogeneous volume

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Multivectoris adimension of the vector space V.Linearity in either input together with the alternating property implies linearity in the other input0.90text
Multivectorrelated to Clifford productClifford0.60section
Multivectorrelated to Clifford productHamilton's0.60section
Multivectorrelated to Clifford productThe Clifford0.60section
Multivectorrelated to Clifford productClifford's0.60section
Multivectorrelated to Exterior productThe0.60section
Multivectorrelated to Exterior productThis0.60section
Multivectorrelated to Exterior productLinear0.60section
Multivectorrelated to Exterior productAssociative0.60section
Multivectorrelated to Exterior productAlternating0.60section
Multivectorrelated to Geometric algebraThe0.60section
Multivectorrelated to Geometric algebraClifford Algebra0.60section

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