Decompositions

Abstract

A vector field is a notion in multidimensional analysis. Specifically, to point x in a domain $G\;\subset\;\mathbb{R}^n$ one assigns a vector ${\bf{ u}}(x)\;=\;(u_1,\ldots,u_n)^T$. Vector fields play an important role in the description of physical relevant equations in the plane and space. In particular, vector fields describe the intensity and direction of a force, the velocity and direction of particles in a moving fluid, or the magnitude and direction of electric and magnetic forces.