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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Levi-Civita symbol (redirect from Antisymmetric symbol)
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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Penrose graphical notation (redirect from Tensor diagram 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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Ricci calculus (redirect from Tensor calculus)
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...
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Relativistic angular momentum (redirect from Angular momentum tensor)
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...
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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
Exterior algebra (section Alternating tensor 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
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...
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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
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
torque, also second order antisymmetric tensor. The electromagnetic field tensor is another second order antisymmetric tensor field, with six components:...
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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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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...
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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...
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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...
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Kronecker delta (redirect from Kronecker tensor)
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...
19 KB (3,665 words) - 03:46, 24 June 2025
Ricci curvature (redirect from Ricci curvature tensor)
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
Moment of inertia (redirect from Moment of inertia tensor)
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