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Tensor product

In mathematics, the tensor product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W {\displaystyle V\times W\rightarrow V\otimes W} that maps a pair ( v , w ) {\displaystyle (v,w)} , where v ∈ V , w ∈ W…

Products, Definitions and constructions & Other examples of tensor products

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Definitions and constructions

Up toIsomorphismUniversal propertyObjectsFunctions
18 related topics

Other examples of tensor products

Hilbert spacesAn analogous operationSymmetric monoidal categoryMetric space completionHilbert–Schmidt operators
14 related topics

Tensor product of linear maps

Category theoryBifunctorCategoryInjectiveSurjective
13 related topics

Tensor products of modules over a ring

ModulesCommutativeFree R-moduleNon-commutativeAbelian group
12 related topics

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Overview

Definitions and constructions

Properties

Tensor product of linear maps

General tensors

Linear maps as tensors

Tensor products of modules over a ring

Tensor product of algebras

Eigenconfigurations of tensors

Other examples of tensor products

Quotient algebras

Tensor product in programming

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Tensor product

Nodes136
Edges135
Triples147
Avg. degree1.99
Density0.014706
Components1

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Tensor product

Top relations

related to References · 48
Tensor product → Abstract Algebra, Aguiar, Algebra, AMS Chelsea, Archived, Bibliography, Birkhoff, Bourbaki, Business Media, CRM Monograph Series Vol, Distributions, Dover Publications, Elements, Finite, François, Gowers, Graduate Texts, Grillet, Halmos, Hopf
related to Tensor product of algebras · 9
Tensor product → A-algebra, For, Galois, In, Let, R-algebra, R-algebras, R-modules, The
related to Array programming languages · 7
Tensor product → APL, Array, BorA, For, In, J's, This
related to Computing the tensor product · 7
Tensor product → For, M/nM, More, R-module, The, Z-module, Z/nZ
is a · 6
Tensor product → bifunctor from the category of vector spaces to itself.If f and g are both injective or surjective, dyadic form of, generalization of the outer product, monoidal category, multilinear form, right exact functor
related to Definitions and constructions · 6
Tensor product → As, Most, The, There, Universal, When
related to Topological tensor products · 6
Tensor product → Hilbert, However, In, It, Schmidt, There
see also · 6
Tensor product → Category, Dyadics, Operation, Second, Tensor, Universal
related to Tensor product of graphs · 5
Tensor product → Compare, However, It, Kronecker, Tensor
related to Tensor products of modules over a ring · 5
Tensor product → If, In, More, R-module, The

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Important terminology

tensor displaystyle product otimes vector two spaces map space times linear basis maps defined given bases field universal products bilinear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tensor productis ageneralization of the outer product0.90text
Tensor productis abifunctor from the category of vector spaces to itself.If f and g are both injective or surjective0.90text
Tensor productis aright exact functor0.90text
Tensor productis amultilinear form0.90text
Tensor productis amonoidal category0.90text
Tensor productis adyadic form of0.90text
the Jacobian derivativeinstance ofand/or may not support higher-order functions0.80text
Tensor productrelated to Adjoint representationThe0.60section
Tensor productrelated to Adjoint representationLie0.60section
Tensor productrelated to Adjoint representationEnd0.60section
Tensor productrelated to Adjoint representationThere0.60section
Tensor productrelated to Array programming languagesArray0.60section

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