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...
11 KB (1,823 words) - 05:49, 19 May 2025
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...
50 KB (8,677 words) - 07:36, 29 May 2025
vector fields in Physics), and ⊗ {\displaystyle \otimes } is the tensor product of vector bundles. Equivalently, a tensor field is a collection of elements...
26 KB (4,401 words) - 17:09, 26 May 2025
glossary of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...
8 KB (1,034 words) - 11:00, 27 October 2024
of differential operators. Tor functor Tensor product of algebras Tensor product of fields Derived tensor product Eilenberg–Watts theorem Tensoring with...
48 KB (8,469 words) - 09:18, 29 May 2025
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...
6 KB (1,062 words) - 10:27, 3 February 2025
(stress–energy tensor, curvature tensor, ...). In applications, it is common to study situations in which a different tensor can occur at each point of an object;...
69 KB (9,357 words) - 17:01, 16 June 2025
over a field (or other commutative ring) Tensor product of representations, a special case in representation theory Tensor product of fields, an operation...
2 KB (261 words) - 16:01, 22 May 2023
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...
23 KB (3,727 words) - 16:43, 13 June 2025
electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...
18 KB (3,463 words) - 17:22, 24 April 2025
component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties...
11 KB (1,719 words) - 12:38, 26 May 2025
stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...
25 KB (4,040 words) - 17:23, 6 February 2025
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...
56 KB (8,863 words) - 21:58, 19 May 2025
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...
13 KB (1,888 words) - 02:15, 5 June 2025
learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data...
31 KB (4,104 words) - 16:37, 16 June 2025
Dirichlet's unit theorem (redirect from Regulator of an algebraic number field)
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 ⊗...
13 KB (1,756 words) - 14:22, 15 February 2025
of which one can recognise categories of G-sets for G profinite. To see how this applies to the case of fields, one has to study the tensor product of...
4 KB (593 words) - 23:45, 13 February 2025
reduced rings Dual numbers Tensor product of fields Tensor product of R-algebras Quotient ring Field of fractions Product of rings Annihilator (ring theory)...
4 KB (296 words) - 00:44, 5 February 2025
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno...
19 KB (2,934 words) - 18:43, 20 December 2024
In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group...
16 KB (2,941 words) - 05:49, 19 May 2025
indeterminates ai, E is any field, and n ≥ 5). The tensor product of fields is not usually a field. For example, a finite extension F / E of degree n is a Galois...
87 KB (10,305 words) - 21:38, 10 June 2025
Separable polynomial (category Field (mathematics))
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...
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Dyadics (redirect from Dyadic tensor)
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...
29 KB (4,634 words) - 00:11, 27 July 2024
of a common field then the (external) composite is defined using the tensor product of fields. Note that some care has to be taken for the choice of the...
4 KB (886 words) - 07:16, 16 June 2025
Ricci calculus (redirect from Tensor calculus)
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...
46 KB (7,275 words) - 11:43, 2 June 2025
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting...
7 KB (760 words) - 06:09, 26 May 2025
In functional analysis, an area of mathematics, the injective tensor product is a particular topological tensor product, a topological vector space (TVS)...
13 KB (2,518 words) - 04:14, 13 March 2025
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...
41 KB (6,211 words) - 12:34, 3 June 2025
In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T (...
11 KB (1,794 words) - 09:27, 10 February 2025
Ricci curvature (redirect from Ricci curvature tensor)
between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a...
34 KB (5,863 words) - 23:45, 30 December 2024