Way to express a general vector field

0rthodontist

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

HallsofIvy

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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.
 

0rthodontist

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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.
 

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