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Way to express a general vector field 
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#1
Apr1806, 08:33 PM

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P: 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
Apr1906, 07:29 AM

Math
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Thanks
PF Gold
P: 39,363

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
Apr1906, 07:31 AM

Sci Advisor
P: 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.



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