# Jacobian matrix generalization in coordinate transformation

• I
hi, I always see that jacobian matrix is derived for just 2 dimension ( ıt means 2x2 jacobian matrix) in books while ensuring the coordinate transformation. After that kind of derivation, books say that you can use same principle for higher dimensions. But, I really wonder if there is a proof which ensure that jacobian matrix is compatible with higher dimensions???? I am asking because there are proofs which ensure the jacobian matrix only in 2 dimensions not higher dimensions.. Thanks in advance.... I am looking forward to your mathematical demonstrations....

andrewkirk
Homework Helper
Gold Member
Jacobian matrices have several useful properties.
For which one of those properties are you seeking a proof?

Jacobian matrices have several useful properties.
For which one of those properties are you seeking a proof?
While doing integral in terms of space-time coordinates, and if you want to change coordinates, we should use jacobian matrix and determinant rule. I know the proof of why we should use jacobian determinant rule if there are 2 coordinates, but I do not know the proof of how this jacobian determinant rule fits with the higher dimensions or high order coordinates ????

I hope my question has become explicit after my last post...

Is there someone who can answer my question ?????? :D I am really looking forward to your answers ......

andrewkirk