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## Main Question or Discussion Point

I'm not sure if this belongs in physics or here. Consider the transformation of a vector from one coordinate system to the other. I can write:

V

V

In each case are the partials equivalent to the Jacobean matrices? Also, what about the case of a tensor

T

Is the transformation just the product of 2 Jacobeans?

V

^{n}= (∂y^{n}/∂x^{m})V^{m}- contravariant formV

_{n}= (∂x^{m}/∂y^{n})V_{m}- covariant formIn each case are the partials equivalent to the Jacobean matrices? Also, what about the case of a tensor

T

_{mn}= (∂x^{r}/∂y^{m})(∂x^{s}/∂y^{n})T_{rs}Is the transformation just the product of 2 Jacobeans?