is built into the notation. The result is another tensor with order reduced by 2. Tensor contraction can be seen as a generalization of the trace. Let...

a chain of N tensors of order 2 or 3, which gives us a polynomial number of parameters. Tensor Tensor diagrams Tensor contraction Tensor Processing Unit...

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...

the trace of a tensor t = t a b c {\displaystyle t=t_{ab}{}^{c}} over its last two slots. This manner of representing tensor contractions by repeated indices...

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

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...

routing Contraction mapping, a type of function on a metric space Edge contraction or vertex contraction, graph operations used in graph theory Tensor contraction...

Riemann tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction on any...

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

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...

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...

The Tensor Contraction Engine (TCE) is a compiler for a domain-specific language that allows chemists to specify the computation in a high-level Mathematica-style...

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...

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

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...

to arbitrary tensor fields, in a unique way that ensures compatibility with the tensor product and trace operations (tensor contraction). Given a point...

In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space...

the contraction with a tensor B that is symmetric on indices i {\displaystyle i} and j {\displaystyle j} is identically 0. For a general tensor U with...

differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors...

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...

tensor tympani muscle in the middle ear as part of the startle response to some sounds. This lowered reflex threshold for tensor tympani contraction is...

Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor contraction Symmetric algebra, Symmetric power Symmetric tensor Mixed tensor Pandey, Divyanshu;...

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...

dot productPages displaying short descriptions of redirect targets Tensor contraction – Operation in mathematics The character ⨼ is U+2A3C INTERIOR PRODUCT...

similar to MATLAB and GNU Octave, but designed specifically for tensors. Tensor is a tensor package written for the Mathematica system. It provides many...

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

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

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...

a tensor of order n {\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle n+m-2} , see Tensor contraction...

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