Jacobean matrix

  • Thread starter nigelscott
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  • #1
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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:

Vn = (∂yn/∂xm)Vm - contravariant form

Vn = (∂xm/∂yn)Vm - covariant form

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

Tmn = (∂xr/∂ym)(∂xs/∂yn)Trs

Is the transformation just the product of 2 Jacobeans?
 

Answers and Replies

  • #2
Bacle2
Science Advisor
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Yes, the Jacobian is used to describe coordinate changes. Is that what you

were asking?
 
  • #3
134
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Yes. I wasn't quite sure if there were any implications associated with covariant versus contravariant vectors in differential geometry. Also, in the case of a tensor, I wasn't sure if the transformation was the product of the Jacobean with it's inverse or transpose.
 
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