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For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

The normalized vector of X is a vector in the same direction but with norm (length) 1. It is denoted X^^ and given by X^^=(X)/(|X|), where |X| is the norm of X. It is also ...

A topological space X in which each subset of X of the "first category" has an empty interior. A topological space which is homeomorphic to a complete metric space is a Baire ...

A vector sum is the result of adding two or more vectors together via vector addition. It is denoted using the normal plus sign, i.e., the vector sum of vectors A, B, and C ...

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

n-dimensional Euclidean space.

There are two different definitions of "polar vector." In elementary math, the term "polar vector" is used to refer to a representation of a vector as a vector magnitude ...

A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...

A zero vector, denoted 0, is a vector of length 0, and thus has all components equal to zero. It is the additive identity of the additive group of vectors.