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Two nonsingular forms are equivalent over the rationals iff they have the same determinant and the same p-signatures for all p.

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

Orthogonal contravariant and covariant satisfy g_(ik)g^(ij)=delta_k^j, where delta_j^k is the Kronecker delta.

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

p^~=|phi_i(x)><phi_i(t)| (1) p^~sum_(j)c_j|phi_j(t)>=c_i|phi_i(x)> (2) sum_(i)|phi_i(x)><phi_i(x)|=1. (3)

A quantity which transforms like a tensor except for a scalar factor of a Jacobian.

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

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...