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# Acronyms that contain the term **tensor product**

#### What does **tensor product** mean? This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: **tensor product**.

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#### What does **tensor product** mean?

- Tensor product
- In mathematics, the tensor product V ⊗ W of two vector spaces V and W (over the same field) is itself a vector space, endowed with the operation of bilinear composition, denoted by ⊗, from ordered pairs in the Cartesian product V × W to V ⊗ W in a way that generalizes the outer product. Essentially the difference between a tensor product of two vectors and an ordered pair of vectors is that if one vector is multiplied by a nonzero scalar and the other is multiplied by the reciprocal of that scalar, the result is a different ordered pair of vectors, but the same tensor product of two vectors, and that the pairs of vectors are added one coordinate at a time (with the other coordinate being the same throughout) rather than both coordinates at the same time - all as one would expect if the vectors were "directly multiplied" in some sense, the tensor product making this idea precise. The tensor product of V and W is the vector space generated by the symbols v ⊗ w, with v ∈ V and w ∈ W, in which the relations of bilinearity are imposed for the product operation ⊗, and no other relations are assumed to hold. The tensor product space is thus the "freest" (or most general) such vector space, in the sense of having the fewest constraints.

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