Tensorproduct
In mathematics , the tensorproduct , denoted by math otimes math , may be applied in different contexts ..., this product is also referred to as outer product . The term tensorproduct is also used in relation ..
Tensorproduct of algebras
In mathematics , the tensorproduct of two algebra ring theory R algebras is also an R algebra in a natural way. This gives us a tensorproduct of algebras . The special case R Z gives us a tensorproduct ..
Tensorproduct of graphs
Image Graph tensor product.svg thumb 360px The tensorproduct of graphs. In graph theory , the tensor ... is adjacent with v . The tensorproduct is also called the direct product , categorical product , cardinal ..
Tensorproduct network
A tensorproduct 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 tensorproduct of these vectors ..
Tensorproduct of quadratic forms
Unreferenced date February 2008 The tensorproduct of quadratic form s is most easily understood when ... V,W vector spaces, then the tensorproduct is a quadratic form q on the Tensorproducttensor ..
Topological tensorproduct
In mathematics , there are usually many different ways to construct a topological tensorproduct of two ... theory of tensorproduct s, but for general Banach space s or locally convex topological vector space ..
Tensorproduct of modules
In mathematics , the tensorproduct of modules is a construction that allows arguments about bilinear ... s . The module construction is analogous to the construction of the tensorproduct of vector space ..
Tensorproduct of fields
are both field extension s of a smaller field N for example a prime field . The tensorproduct of fields ... common subfields of a field M . Correspondingly their tensorproduct will in that case be the zero ..
Relative tensorproduct
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 ...
Tensor
of covariant and contravariant indices. Expressed by means of the tensorproduct of multilinear algebra, this is the number of factors of the tensorproduct needed to express T . In the second definition ..
Product
wiktionarypar productProduct 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 ..
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 ..
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 ..
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 ..
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 ..
Dyadic tensor
is an elementary tensor in the tensorproduct of V with its dual space. The tensorproduct of V and its ... product to identify the dual space with V itself, making a dyadic tensor an elementary tensorproduct ..
Tensor contraction
is the linear transformation from the Component free treatment of tensors Definition TensorProduct of Vector Spaces tensorproduct of these two spaces to the field k math C V otimes V rightarrow k ..
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 TensorTensor rank rank three. It vanishes for the case ..
Tensor field
M , a choice of vector v sub m sub in V sub m sub , the vector space at m . Since the tensorproduct concept is independent of any choice of basis, taking the tensorproduct of two vector bundles on M ..
Tensor algebra
over a field algebra of tensor s on V of any rank with multiplication being the tensorproduct ... sup th sup tensor power of V to be the tensorproduct of V with itself k times math T kV V otimes ..
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 ..
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 ..
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 ..
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 ..
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 ..