Tensorproduct
In mathematics , the tensorproduct , denoted ref The symbol was used much earlier for the Phoenician ... to as outer product . The term tensorproduct is also used in relation to monoidal category monoidal ..
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 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 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 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 Hilbert spaces
In mathematics , and in particular functional analysis , the tensorproduct of Hilbert space s is a way to extend the tensorproduct construction so that the result of taking a tensorproduct of two Hilbert ..
Tensorproduct of fields
s of a smaller field N for example a prime field . The tensorproduct of fields is the best available ... M . Correspondingly their tensorproduct will in that case be the trivial ring collapse of the construction ..
Tensor
geometry , a tensor is first of all an element of a tensorproduct of vector space s. In physics ... in each is a matrix, while the outer product of three or more vectors is a tensor. Similarly ..
Product
wiktionarypar productProduct 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 ..
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 ..
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 a measure of the curvature ... tensor , the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic ..
Tensor density
zero is an ordinary tensor. A tensor density can also be regarded as a section of the tensorproduct ...In differential geometry , a tensor density transforms as a tensor when passing from one coordinate system ..
Tensor field
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 is routine ..
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 contraction Product of Vector Spaces tensorproduct 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 tensorproduct math T otimes ..
Symmetric tensor productTensor 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 tensorproduct math T v 1 otimes v 2 otimes cdots ..
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 ..
Tensor algebra
being the tensorproduct . 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 tensorproduct of V with itself k ..
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 tensorproduct of V with its dual space. The tensor ..
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 ..
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 ..