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## Main Question or Discussion Point

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....