 Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence (which represents the rate of change of volume of a flow) and curl (which represents the rotation of a flow).In coordinates, a vector field on a domain in "n"-dimensional Euclidean space can be represented as a vector-valued function that associates an "n"-tuple of real numbers to each point of the domain.This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other.