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In a paper they say that a certain quantity is a rank-2 tensor because it transforms like a spin-2 object under rotations, that is: if the basis vectors undergo a rotation of angle [itex]\phi[/itex], then this quantity, say A, transforms like

[itex]A\mapsto Ae^{i2\phi}[/itex]

As far as I knew, a rank-2 tensor is a 2-linear functions or vectors or one forms. In the case it is, for example, completely covariant, it will transform like

[itex]T'_{ij}=\frac{\partial x^{'a}}{\partial x^i}\frac{\partial x^{'b}}{\partial x^j}T_{ab}[/itex]

What is the link between the two definitions? Why should a spin-2 object be a tensor?

Thanks in advance!

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# Rank-2 tensor: multiple definitions

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