Transformations and their inverse

[FunkyDwarf]

Hey guys

This isn't related to a particular question but i thought might be too specific for the general forum so here we go...

If you have a function f(x,y) such that u = f(x) and v= g(x) and you have some transformation T(u,v) i know you can find the inverse by getting x and y in terms of u and v and getting the Jacobian matrix etc. BUT if you can't (or like me too lazy/stupid) to be able to find f-1 or g-1 then is there a shortcut? I ask this knowing half the answer: i remembe there being a relation between the jacobian for a transform and its inverse but i don't know what it is.

The reason i ask the rest of the shpeel before it is to make sure I am understanding that correctly as well.

Thanks
-G

 

[chesshaha]

There's no shortcut...

 

[FunkyDwarf]

Ah finally found what i think it is:

Remark: A useful fact is that the Jacobian of the inverse transformation is the reciprocal of the Jacobian of the original transformation.

Is this not true?