tensor product
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English
[edit]Noun
[edit]tensor product (plural tensor products)
- (mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.
- 2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra[1], →ISBN, →OCLC, page 421:
- Linear Transformations on Tensor Products of Vector Spaces
- [...]
- Proposition 16. Let V and W be finite dimensional vector spaces over the field F with bases and respectively. Then is a vector space over F of dimension nm with basis , and .
- 2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila)[2], spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube:
- [The tensor product] is the span of
modulo the relations
- [The tensor product] is the span of
Usage notes
[edit]- The ⊗ symbol can be read out as “tensor”.
Hyponyms
[edit]Meronyms
[edit]- tensor (if the tensor product is between algebraic structures)
Holonyms
[edit]Translations
[edit]bilinear operation
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