Encyclopedia results for Tensor product

1. Tensor product
   
   In mathematics , the tensor product , denoted by math otimes math , may be applied in different contexts ..., this product is also referred to as outer product . The term tensor product is also used in relation ..
   
   
   
   
2. Tensor product of algebras
   
   In mathematics , the tensor product of two algebra ring theory 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 ..
   
   
   
   
3. Tensor product of graphs
   
   Image Graph tensor product.svg thumb 360px The tensor product of graphs. In graph theory , the tensor ... is adjacent with v . The tensor product is also called the direct product , categorical product , cardinal ..
   
   
   
   
4. Tensor product network
   
   A tensor product network , in neural network s, is a network that exploits the properties of tensor s to model ... the ideas such as variable names and target assignments , and the tensor product of these vectors ..
   
   
   
   
5. Tensor product of quadratic forms
   
   Unreferenced date February 2008 The tensor product of quadratic form s is most easily understood when ... V,W vector spaces, then the tensor product is a quadratic form q on the Tensor product tensor ..
   
   
   
   
6. Topological tensor product
   
   In mathematics , there are usually many different ways to construct a topological tensor product of two ... theory of tensor product s, but for general Banach space s or locally convex topological vector space ..
   
   
   
   
7. Tensor product of modules
   
   In mathematics , the tensor product of modules is a construction that allows arguments about bilinear ... s . The module construction is analogous to the construction of the tensor product of vector space ..
   
   
   
   
8. Tensor product of fields
   
   are both field extension s of a smaller field N for example a prime field . The tensor product of fields ... common subfields of a field M . Correspondingly their tensor product will in that case be the zero ..
   
   
   
   
9. Relative tensor product
   
   Let math A math be a right R module mathematics module and math B math be a left R module mathematics module see the definition of left and right module in module mathematics . The relative tensor pro ...
   
   
   
   
10. Tensor
    
    of covariant and contravariant indices. Expressed by means of the tensor product of multilinear algebra, this is the number of factors of the tensor product needed to express T . In the second definition ..
    
    
    
    
11. Product
    
    wiktionarypar product Product may mean Product biology , something manufactured by an organelle Product business , an item that ideally satisfies a market s want or need Product chemistry , a substance ..
    
    
    
    
12. By-product
    
    A by product is a secondary or incidental product deriving from a manufacturing process, a chemical reaction or a biochemical pathway, and is not the primary product or service being produced. A by product ..
    
    
    
    
13. Schouten tensor
    
    the Riemann curvature tensor minus the Kulkarni&ndash Nomizu product of the Schouten tensor with the metric ...In mathematics , more specifically Riemannian geometry , the Schouten tensor is for n 3 dimensions, math ..
    
    
    
    
14. Weyl tensor
    
    In differential geometry , the Weyl curvature tensor , named after Hermann Weyl , is the traceless component of the Curvature tensor Riemann curvature tensor . In other words, it is a tensor that has the same ..
    
    
    
    
15. Tensor density
    
    A tensor density transforms as a tensor , except that it is additionally multiplied or weighted by a power of the Jacobian determinant. For example, a rank 3 tensor density of weight W transforms as math ..
    
    
    
    
16. Dyadic tensor
    
    is an elementary tensor in the tensor product of V with its dual space. The tensor product of V and its ... product to identify the dual space with V itself, making a dyadic tensor an elementary tensor product ..
    
    
    
    
17. Tensor contraction
    
    is the linear transformation from the Component free treatment of tensors Definition Tensor Product of Vector Spaces tensor product of these two spaces to the field k math C V otimes V rightarrow k ..
    
    
    
    
18. Nonmetricity tensor
    
    In mathematics , the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor . It is therefore a tensor field of Tensor Tensor rank rank three. It vanishes for the case ..
    
    
    
    
19. Tensor field
    
    M , a choice of vector v sub m sub in V sub m sub , the vector space at m . Since the tensor product concept is independent of any choice of basis, taking the tensor product of two vector bundles on M ..
    
    
    
    
20. Tensor algebra
    
    over a field algebra of tensor s on V of any rank with multiplication being the tensor product ... sup th sup tensor power of V to be the tensor product of V with itself k times math T kV V otimes ..
    
    
    
    
21. Stress tensor
    
    For the stress tensor in classical physics , see the article stress physics . For the stress tensor in theory of relativity relativistic theories, see stress energy tensor . For the stress tensor in electromagnetism ..
    
    
    
    
22. Electromagnetic tensor
    
    right mathrm invariant math The product of the tensor math F mu nu , math with its dual tensor gives ...Electromagnetism cTopic Theory of relativity Covariant formulation The electromagnetic tensor or electromagnetic ..
    
    
    
    
23. Topogravitic tensor
    
    In general relativity , the topogravitic tensor is one of the three pieces of the Bel decomposition of the Riemann tensor . The topogravitic tensor can be interpreted as representing the sectional curvatures ..
    
    
    
    
24. Tensor bundle
    
    Unreferenced date August 2008 In mathematics , the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold. To do calculus on the tensor ..
    
    
    
    
25. Contorsion tensor
    
    The contorsion tensor in differential geometry expresses the effect of the torsion tensor on the Christoffel symbol and the spin connection . The contorsion tensor math K c ab math is defined in terms ..
    
    
    
    

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