to in the shorter form "tensor". For example, the Riemann curvature tensor refers a tensor field, as it associates a tensor to each point of a Riemannian...

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

(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In...

In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. An example of...

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...

stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...

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...

numbers), and a 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...

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

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

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...

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...

covariant derivative of a tensor field along a vector field v is again a tensor field of the same type. Explicitly, let T be a tensor field of type (p, q). Consider...

element for the tensor space. The tensor is the sum of its components multiplied by their corresponding basis elements. Tensors and tensor fields can be expressed...

electromagnetic field, spinor fields whose quanta are fermionic particles such as electrons, and tensor fields such as the metric tensor field that describes...

Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum...

In theoretical particle physics, the gluon field strength tensor is a second order tensor field characterizing the gluon interaction between quarks. The...

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...

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...

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

together all the tensors at all points of the manifold, thus 'bundling' them all into one grand object called the tensor bundle. A tensor field is then defined...

the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It is therefore a tensor field of order three. It...

the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is...

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

associate a tensor to every point in space. For example, in general relativity gravitation is associated with the tensor field called Einstein tensor. In Kaluza–Klein...

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...

package the E and B fields into what is known as the electromagnetic tensor F μ ν {\displaystyle F_{\mu \nu }} . We define this tensor as F μ ν = ∂ μ A ν...

manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted...

coordinates at Wolfram Mathworld Gurtin 1981, p. 30. "1.14 Tensor Calculus I: Tensor Fields" (PDF). Foundations of Continuum Mechanics. Archived (PDF)...

Scribner's Sons. pp. 159, 161–162. Kelly, P. (2013). "Chapter 1.14 Tensor Calculus 1: Tensor Fields" (PDF). Mechanics Lecture Notes Part III: Foundations of Continuum...