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 (...

permutation object acting on tensors Ricci calculus – Tensor index notation for tensor-based calculations Symmetric tensor – Tensor invariant under permutations...

Symmetric power, symmetric algebra This is the invariant way of constructing polynomial algebras. Metric tensor Strain tensor Stress–energy tensor Jacobian...

The metric tensor is an example of a tensor field. The components of a metric tensor in a coordinate basis take on the form of a symmetric matrix whose...

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

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...

endomorphism of Tn(V). A symmetric tensor is a tensor that is invariant under all these endomorphisms. The symmetric tensors of degree n form a vector...

the tensor g {\displaystyle g} is a tensor field, which is defined at all points of a spacetime manifold). In order for the metric to be symmetric g μ...

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...

stress tensor will be symmetric. As with any symmetric tensor, the viscous stress tensor ε can be expressed as the sum of a traceless symmetric tensor εs...

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...

of the corresponding symmetric tensor κ i j ⋯ k {\displaystyle \kappa ^{ij\cdots k}} , this condition is equivalent to the tensor being invariant: f i...

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

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

In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e.,...

The tensor algebra is important because many other algebras arise as quotient algebras of T(V). These include the exterior algebra, the symmetric algebra...

Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a symmetric bilinear...

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...

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...

notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names...

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...

strain tensor is defined by the IUPAC as: "A symmetric tensor that results when a deformation gradient tensor is factorized into a rotation tensor followed...

principal values of the symmetric part of A {\displaystyle \mathbf {A} } . Even though the eigenvalues of a real non-symmetric tensor might be complex, the...

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

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

field is characterized by a symmetric rank-2 tensor, the metric tensor. The possibility of generalizing the metric tensor has been considered by many...

elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness...

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...

Cauchy stress tensor (symbol ⁠ σ {\displaystyle {\boldsymbol {\sigma }}} ⁠, named after Augustin-Louis Cauchy), also called true stress tensor or simply stress...

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...