Antisymmetric tensor information

completely antisymmetric contravariant tensor field may be referred to as a k {\displaystyle k} -vector field. A tensor A that is antisymmetric on indices...

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...

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...

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 , v...

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...

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...

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...

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

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...

The electromagnetic tensor is the combination of the electric and magnetic fields into a covariant antisymmetric tensor whose entries are B-field...

two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense...

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

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...

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...

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...

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...

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...

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...

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...

differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...

essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting...

i_{r-1}}} 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...

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...

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

universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. The tensor product of an algebra and...

torque, also second order antisymmetric tensor. The electromagnetic field tensor is another second order antisymmetric tensor field, with six components:...