• completely antisymmetric contravariant tensor field may be referred to as a k {\displaystyle k} -vector field. A tensor A that is antisymmetric on indices...
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  • independent of any metric tensor and coordinate system. Also, the specific term "symbol" emphasizes that it is not a tensor because of how it transforms...
    30 KB (5,174 words) - 23:34, 10 July 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 (...
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  • that B(x, y) = −B(y, x) for all x and y. Antisymmetric tensor in matrices and index subsets. "antisymmetric function" – odd function Symmetry in mathematics...
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  • Thumbnail for Penrose graphical notation
    essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting...
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  • 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...
    46 KB (7,275 words) - 11:43, 2 June 2025
  • Thumbnail for Relativistic angular momentum
    or alternatively as the exterior product to obtain a second order antisymmetric tensor x ∧ p. What does this combine with, if anything? There is another...
    57 KB (10,973 words) - 18:06, 24 June 2025
  • calculus on the tensor bundle a connection is needed, except for the special case of the exterior derivative of antisymmetric tensors. A tensor bundle is a...
    1 KB (222 words) - 06:34, 6 April 2023
  • Thumbnail for Tensor
    to get a maximally covariant antisymmetric tensor. Raising an index on an (n, m)-tensor produces an (n + 1, m − 1)-tensor; this corresponds to moving diagonally...
    69 KB (9,437 words) - 13:06, 15 July 2025
  • Thumbnail for Exterior algebra
    be an antisymmetric tensor of rank ⁠ r {\displaystyle r} ⁠. Then, for α ∈ V∗, ⁠ ι α t {\displaystyle \iota _{\alpha }t} ⁠ is an alternating tensor of rank...
    77 KB (12,242 words) - 02:39, 1 July 2025
  • Thumbnail for Curl (mathematics)
    limitations of vector calculus; on the other hand, when expressed as an antisymmetric tensor field via the wedge operator of geometric calculus, the curl generalizes...
    34 KB (5,050 words) - 04:31, 3 May 2025
  • Thumbnail for Covariant formulation of classical electromagnetism
    The electromagnetic tensor is the combination of the electric and magnetic fields into a covariant antisymmetric tensor whose entries are B-field...
    25 KB (4,013 words) - 14:23, 26 June 2025
  • 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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  • tensor field is found to satisfy the equations of a Maxwell–Proca massive antisymmetric tensor field. This led Moffat to propose metric-skew-tensor-gravity...
    5 KB (573 words) - 11:21, 25 May 2024
  • Thumbnail for Special relativity
    torque, also second order antisymmetric tensor. The electromagnetic field tensor is another second order antisymmetric tensor field, with six components:...
    186 KB (24,928 words) - 17:50, 17 July 2025
  • 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
  • pseudovectors and antisymmetric tensors of order 2. The dual of a pseudovector is an antisymmetric tensor of order 2 (and vice versa). The tensor is an invariant...
    6 KB (831 words) - 20:55, 21 May 2025
  • 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...
    56 KB (8,863 words) - 21:58, 19 May 2025
  • The electromagnetic field tensor F a b {\displaystyle F^{ab}} , a rank-two antisymmetric tensor. Although the word 'tensor' refers to an object at a point...
    42 KB (7,044 words) - 06:10, 20 January 2025
  • manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted...
    15 KB (2,490 words) - 23:17, 5 July 2025
  • the 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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  • The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed...
    17 KB (2,581 words) - 17:04, 14 March 2025
  • 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...
    11 KB (1,719 words) - 12:38, 26 May 2025
  • 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...
    23 KB (3,727 words) - 16:43, 13 June 2025
  • mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...
    19 KB (2,934 words) - 18:43, 20 December 2024
  • and ♯ maps k-covectors to k-vectors, all the indices of a totally antisymmetric tensor are simultaneously raised or lowered, and so no index need be indicated:...
    20 KB (4,149 words) - 23:22, 17 July 2025
  • Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann...
    10 KB (1,742 words) - 18:26, 17 March 2025
  • thought of as a tensor, and is written δ j i {\displaystyle \delta _{j}^{i}} . Sometimes the Kronecker delta is called the substitution tensor. In the study...
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  • relationship between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of...
    34 KB (5,807 words) - 20:11, 6 July 2025
  • Thumbnail for Moment of inertia
    inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of...
    91 KB (17,178 words) - 02:19, 5 July 2025