Tensor product (disambiguation)
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Tensor Product refers to one of several related binary operations, typically denoted . Usually, they are associative, unital, and symmetric (up to some appropriate kind of structural equivalence).
It may refer to:
- Tensor product of vector spaces, an operation on vector spaces (the original tensor product)
- Tensor product of modules, the same operation slightly generalized to modules over arbitrary rings
- Kronecker product, the tensor product of matrices (or vectors), which satisfies all the properties for vector spaces and allows a concrete representation
- Tensor product of Hilbert spaces, endowed with a special inner product as to remain a Hilbert space
- Tensor product of graphs, an operation on graphs, whose adjacency matrices are the
- Tensor product of algebras (or rings), on algebras over a field (or other commutative ring)
- Tensor product of representations, a special case in representation theory
- Tensor product of fields, an operation on fields—unlike most tensor products, the category of fields is not closed with respect to this operation (i.e., sometimes the product is not a field)
- "Categorified" concepts, applied "pointwise" on objects and morphisms:
- Tensor product of vector bundles
- Tensor product of sheaves of modules, essentially the same thing
- Tensor product of functors
Categories closed under a suitable tensor product are called "monoidal categories". Special types of monoidal categories exist with interesting properties.
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