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

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

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...

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...

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

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...

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...

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...

tensor product is in general not necessarily complete, so its completion is called the completed injective tensor products. Injective tensor products...

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...

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

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

tensor") may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition can factorize data tensors into smaller tensors...

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...

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...

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...

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....

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold...

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:...

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...

calculus Tensor product Product topology Cap product Cup product Slant product Smash product Wedge sum (or wedge product) Internal product, in a monoidal...

{\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle n+m-2} , see Tensor contraction for details...

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 differential geometry, the tensor product of vector bundles E, F (over same space X {\displaystyle X} ) is a vector bundle, denoted by E ⊗ F, whose...

stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...

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...

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...