# Way to express a general vector field

1. ### 0rthodontist

1,253
Is there a simple way to express a general vector field in terms of the gradient of another (perhaps higher dimensional) function?

2. ### HallsofIvy

40,308
Staff Emeritus
Only if it is "exact" (in fact, the definition of "exact" is that it is the derivative of some other function). Even in 2 dimensions, there exist vector fields f(x,y)i+ g(x,y)j that are not graf F for any f.

3. ### 0rthodontist

1,253
I know; I am wondering if there is a way to write vector fields that are not gradients of functions in their own dimension as some simple transformation of a gradient of some function of a higher dimension.