Encyclopedia results for Tensor product

1. Tensor product
   
   In mathematics , the tensor product , denoted ref The symbol was used much earlier for the Phoenician ... to as outer product . The term tensor product is also used in relation to monoidal category monoidal ..
   
   
   
   
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 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 ..
   
   
   
   
4. 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 ..
   
   
   
   
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 Hilbert spaces
   
   In mathematics , and in particular functional analysis , the tensor product of Hilbert space s is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert ..
   
   
   
   
9. Tensor product of fields
   
   s of a smaller field N for example a prime field . The tensor product of fields is the best available ... M . Correspondingly their tensor product will in that case be the trivial ring collapse of the construction ..
   
   
   
   
10. Tensor
    
    geometry , a tensor is first of all an element of a tensor product of vector space s. In physics ... in each is a matrix, while the outer product of three or more vectors is a tensor. Similarly ..
    
    
    
    
11. Product
    
    wiktionarypar product Product may mean Business Product business , an item that ideally satisfies a market s want or need Product breakdown structure Product project management , a deliverable or set of deliverables ..
    
    
    
    
12. By-product
    
    unref article date April 2009 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 ..
    
    
    
    
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 a measure of the curvature ... tensor , the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic ..
    
    
    
    
15. Tensor density
    
    zero is an ordinary tensor. A tensor density can also be regarded as a section of the tensor product ...In differential geometry , a tensor density transforms as a tensor when passing from one coordinate system ..
    
    
    
    
16. Tensor field
    
    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 is routine ..
    
    
    
    
17. 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 ..
    
    
    
    
18. Tensor contraction
    
    Product of Vector Spaces tensor product of these two spaces to the field k math C V otimes V rightarrow ... in a slightly different way, by considering a pair of tensors T and U . The tensor product math T otimes ..
    
    
    
    
19. Symmetric tensor
    
    product Tensor powers and braiding braiding maps associated to every permutation &sigma on the symbols ... r . math If T is a simple tensor, given as a pure tensor product math T v 1 otimes v 2 otimes cdots ..
    
    
    
    
20. Stress tensor
    
    For the stress tensor in classical physics , see the article stress mechanics . For the stress tensor in theory of relativity relativistic theories, see stress energy tensor . For the stress tensor in electromagnetism ..
    
    
    
    
21. Tensor algebra
    
    being the tensor product . It is the free algebra on V , in the sense of being left adjoint to the forgetful ... integer k , we define the k sup th sup tensor power of V to be the tensor product of V with itself k ..
    
    
    
    
22. Dyadic tensor
    
    product associative law associates with the juxtaposition of vectors. The tensor contraction of a dyadic ..., a dyadic tensor on V is an elementary tensor in the tensor product of V with its dual space. The tensor ..
    
    
    
    
23. Electromagnetic tensor
    
    independent components. If one forms an inner product of the field strength tensor a Lorentz invariant ... tensor or electromagnetic field tensor sometimes called the field strength tensor , Faraday ..
    
    
    
    
24. 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 ..
    
    
    
    
25. 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 ..
    
    
    
    

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