multivector
Sign in to saveAlso known as p-vector, polyvector, Clifford number
thumb|Relations between scalars, vectors, simple -vectors, -vectors, and multivectors. Depending on the authors, a "multivector" may be either homogeneous or a mixture of different values of . This graph picks the latter.
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Vinony's link graph records 199 inbound references to multivector, and connects out to differential form, exterior algebra and tensor.
Vinony files it under Differential geometry, Geometric algebra and Multilinear algebra.
Vinony links it to 10 Wikipedia language editions.
Wikidata facts
- Subclass of
- tensor
- Part of
- exterior algebra
- Image
- N vector positive.svg
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- Commons category
- Multivectors
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Encyclopedic overview
14 sectionsContents
- Exterior product
- Area and volume
- Multivectors in R<sup>2</sup>
- Multivectors in R<sup>3</sup>
- Grassmann coordinates
- Multivectors on the projective plane ''P''<sup>2</sup>
- Multivectors on projective 3-space ''P''<sup>3</sup>
- Clifford product
- Geometric algebra
- Examples
- Bivectors
- Applications
- See also
- References
thumb|Relations between scalars, vectors, simple -vectors, -vectors, and multivectors. Depending on the authors, a "multivector" may be either homogeneous or a mixture of different values of . This graph picks the latter.
In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra of a vector space . This algebra is graded, associative and alternating, and consists of linear combinations of simple -vectors (also known as decomposable -vectors or -blades) of the form v_1\wedge\cdots\wedge v_k, where v_1, \ldots, v_k are in .
Excerpted from Wikipedia’s “multivector” article, available under the CC BY-SA 4.0 licence.