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Jacobian transformations watch

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    If I found that the Jacobian of a transformation from say the x-y plane to the u-v plane was f(u, v), would the Jacobian for the transformation from the u-v plane back to the x-y plane be \frac{1}{f(u, v)}?
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    (Original post by Serendreamers)
    If I found that the Jacobian of a transformation from say the x-y plane to the u-v plane was f(u, v), would the Jacobian for the transformation from the u-v plane back to the x-y plane be \frac{1}{f(u, v)}?
    Yes. It's intuitive from the interpretation as "change in the area scale factor" that if you have to blow up by f(u,v) to change coordinates one way, then you have to scale down by the same factor to change coordinates the other way.
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    (Original post by Serendreamers)
    If I found that the Jacobian of a transformation from say the x-y plane to the u-v plane was f(u, v), would the Jacobian for the transformation from the u-v plane back to the x-y plane be \frac{1}{f(u, v)}?
    could not have been explained better by Smaug123!
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    (Original post by TeeEm)
    could not have been explained better by Smaug123!
    Thanks :jumphug:
 
 
 
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