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tensor product

In mathematics, the tensor product V ⊗ W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W that maps a pair ( v , w ) , v ∈ V , w ∈ W to an element of V ⊗ W denoted v ⊗ w. An element of the form v ⊗ w is called the tensor product of v and w. An element of V ⊗ W is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W in the sense that every element of V ⊗ W is a sum of elementary tensors. If bases are given for V and W, a basis of V ⊗ W is formed by all tensor products of a basis element of V and a basis element of W. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Tensor_product)

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