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Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A smooth manifold with a Poisson bracket defined on its function space.

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

A function f is Fréchet differentiable at a if lim_(x->a)(f(x)-f(a))/(x-a) exists. This is equivalent to the statement that phi has a removable discontinuity at a, where ...

Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...