• 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...
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  • 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...
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  • Thumbnail for Tensor field
    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...
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  • 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...
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  • of differential operators. Tor functor Tensor product of algebras Tensor product of fields Derived tensor product Eilenberg–Watts theorem Tensoring with...
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  • over a field (or other commutative ring) Tensor product of representations, a special case in representation theory Tensor product of fields, an operation...
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    (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;...
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  • 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...
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  • Thumbnail for Electromagnetic tensor
    electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...
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  • 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...
    22 KB (3,670 words) - 21:33, 18 March 2025
  • Thumbnail for Stress–energy tensor
    stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...
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  • 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...
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  • 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 ⊗...
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  • 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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  • learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data...
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  • 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...
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  • reduced rings Dual numbers Tensor product of fields Tensor product of R-algebras Quotient ring Field of fractions Product of rings Annihilator (ring theory)...
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  • 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....
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  • 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...
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  • 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 (...
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  • In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno...
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  • 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...
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  • In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group...
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  • In functional analysis, an area of mathematics, the injective tensor product is a particular topological tensor product, a topological vector space (TVS)...
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  • In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting...
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  • Thumbnail for Field (mathematics)
    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
  • 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
  • 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