tensor product
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Tensor product — In mathematics, the tensor product, denoted by otimes, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same:… … Wikipedia
tensor product — tenzorinė sandauga statusas T sritis fizika atitikmenys: angl. tensor product vok. tensorielles Produkt, n; Tensorprodukt, n rus. тензорное произведение, n pranc. produit tensoriel, m … Fizikos terminų žodynas
Tensor product of modules — In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (roughly speaking, multiplication ) to be carried out in terms of linear maps (module homomorphisms). The module construction is analogous… … Wikipedia
Tensor product of graphs — In graph theory, the tensor product G × H of graphs G and H is a graph such that * the vertex set of G × H is the Cartesian product V(G) × V(H) ; and * any two vertices (u,u ) and (v,v ) are adjacent in G × H if and only if u is adjacent with v… … Wikipedia
Tensor product of fields — In abstract algebra, the theory of fields lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to join two fields K and L, either in cases where K and L are … Wikipedia
Tensor product of algebras — In mathematics, the tensor product of two R algebras is also an R algebra in a natural way. This gives us a tensor product of algebras. The special case R = Z gives us a tensor product of rings, since rings may be regarded as Z algebras.Let R be… … Wikipedia
Tensor product of quadratic forms — The tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces . So, if (V, q 1) and (W, q 2) are quadratic spaces, which V,W vector spaces, then the tensor product is a quadratic form q on… … Wikipedia
Tensor product network — A tensor product network, in neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable assignment. Orthonormal vectors are chosen to model the ideas (such as variable names and target… … Wikipedia
Topological tensor product — In mathematics, there are usually many different ways to construct a topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well behaved theory of tensor products (see Tensor product of … Wikipedia
Relative tensor product — Let A be a right R moduleand B be a left R module (see the definition of left and right module in module (mathematics)).The relative tensor product Aotimes R B is defined to be the quotient:Aotimes B/Iwhere I is the ideal generated by all… … Wikipedia
Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… … Wikipedia
