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Way to express a general vector field

by 0rthodontist
Tags: express, field, vector
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0rthodontist
#1
Apr18-06, 08:33 PM
Sci Advisor
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?
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HallsofIvy
#2
Apr19-06, 07:29 AM
Math
Emeritus
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Thanks
PF Gold
P: 39,502
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
#3
Apr19-06, 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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