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:(adsbygoogle = window.adsbygoogle || []).push({});

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

V_{n}= (∂x^{m}/∂y^{n})V_{m}- covariant form

In 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?

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# Jacobean matrix

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