One of the definitions of the tensors says that they are multidimensional arrays of numbers which transform in a certain form under coordinate transformations.No restriction is considered on the coordinate systems involved.So I thought they should transform as such not only under rotations but also under transformation from cartesian to plane polar coordinates,so I tried it on the contravariant tensor below:(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \left(\begin{array}{cc}-xy&-y^{2}\\x^{2}&xy\end{array}\right) [/itex]

But I got zero for all four elements.I got confused then I thought maybe curvilinear coordinates are somehow different from cartesian.Is it correct?If not,what's the reason?

thanks

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# An ambiguity in the definition of tensors

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