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

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...

and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential...

tensor, curvature tensor, ...), and others. In applications, it is common to study situations in which a different tensor can occur at each point of an...

over a field (or other commutative ring) Tensor product of representations, a special case in representation theory Tensor product of fields, an operation...

in the main tensor article. Given a finite set { V1, ..., Vn } of vector spaces over a common field F, one may form their tensor product V1 ⊗ ... ⊗ Vn...

of differential operators. Tor functor Tensor product of algebras Tensor product of fields Derived tensor product Tensoring with M the exact sequence 0...

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 ring is a field, the...

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

A metric tensor g is positive-definite if g(v, v) > 0 for every nonzero vector v. A manifold equipped with a positive-definite metric tensor is known...

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...

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

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...

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

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

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...

In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting...

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

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:...

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

In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T ( v σ 1 ,...

constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection...

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno...

reduced rings Dual numbers Tensor product of fields Tensor product of R-algebras Quotient ring Field of fractions Product of rings Annihilator (ring theory)...

number of real roots and 2r2 is the number of non-real complex roots of f (which come in complex conjugate pairs); write the tensor product of fields K ⊗...

double-dot product (see Dyadics § Product of dyadic and dyadic) however it is not an inner product. The inner product between a tensor of order n {\displaystyle...

perfect. That finite fields are perfect follows a posteriori from their known structure. One can show that the tensor product of fields of L with itself over...

this applies to the case of fields, one has to study the tensor product of fields. In topos theory this is a part of the study of atomic toposes. Tannakian...

{\displaystyle A,B} , resp. are linearly disjoint over k. (cf. Tensor product of fields) Suppose A, B are linearly disjoint over k. If A ′ ⊂ A {\displaystyle...