Search Results for ""

An affine tensor is a tensor that corresponds to certain allowable linear coordinate transformations, T:x^_^i=a^i_jx^j, where the determinant of a^i_j is nonzero. This ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

J_(nualphabeta)^mu=J_(nubetaalpha)^mu=1/2(R_(alphanubeta)^mu+R_(betanualpha)^mu), where R is the Riemann tensor.

The trace of a second-tensor rank tensor T is a scalar given by the contracted mixed tensor equal to T_i^i. The trace satisfies ...

A Cartesian tensor is a tensor in three-dimensional Euclidean space. Unlike general tensors, there is no distinction between covariant and contravariant indices for Cartesian ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The tensor defined by T^l_(jk)=-(Gamma^l_(jk)-Gamma^l_(kj)), where Gamma^l_(jk) are Christoffel symbols of the first kind.

G_(ab)=R_(ab)-1/2Rg_(ab), where R_(ab) is the Ricci curvature tensor, R is the scalar curvature, and g_(ab) is the metric tensor. (Wald 1984, pp. 40-41). It satisfies ...

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

Given an antisymmetric second tensor rank tensor C_(ij), a dual pseudotensor C_i is defined by C_i=1/2epsilon_(ijk)C_(jk), (1) where C_i = [C_(23); C_(31); C_(12)] (2) C_(jk) ...