the tensor product of v {\displaystyle v} and w {\displaystyle w} . An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of...

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms...

(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In...

In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the...

In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the...

product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product...

mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There...

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...

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...

In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group...

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 vertices...

tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product....

projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely...

metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g(v, v) > 0 for...

Tensor product of Hilbert spaces, endowed with a special inner product as to remain a Hilbert space Other topological tensor products Tensor product of...

analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert...

learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data...

have a tensor product. Other kinds of products in linear algebra include: Hadamard product Kronecker product The product of tensors: Wedge product or exterior...

In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space...

differential graded algebra A over a commutative ring R, the derived tensor product functor is − ⊗ A L − : D ( M A ) × D ( A M ) → D ( R M ) {\displaystyle...

differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing...

mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear...

tensor product of vector bundles E, F (over the same space X) is a vector bundle, denoted by E ⊗ F, whose fiber over each point x ∈ X is the tensor product...

injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the underlying...

}_{i_{r+p}}.} The components of this tensor are precisely the skew part of the components of the tensor product s ⊗ t, denoted by square brackets on the...

notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern...

electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...

of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

A tensor product network, in artificial neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable...

The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with:...