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A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

The single bar | is a notation variously used to denote the absolute value |x|, complex modulus |z|, vector norm |x|, determinant |A|, or "divides" (a|b).

The ith Stiefel-Whitney class of a real vector bundle (or tangent bundle or a real manifold) is in the ith cohomology group of the base space involved. It is an obstruction ...

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

A horizontal line placed under a symbol to indicate some special property. Underscores are sometimes used instead of over-arrows or bold typeface to indicate a vector, for ...

The magnitude (length) of a vector x=(x_1,x_2,...,x_n) is given by |x|=sqrt(x_1^2+x_2^2+...+x_n^2).

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

An operation that takes two vector bundles over a fixed space and produces a new vector bundle over the same space. If E_1 and E_2 are vector bundles over B, then the Whitney ...