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According to http://en.wikipedia.org/wiki/Tensor#Tensor_fields,

$\hat{T}^{i_1\dots i_n}_{i_{n+1}\dots i_m}(\bar{x}_1,\ldots,\bar{x}_k) = \frac{\partial \bar{x}^{i_1}}{\partial x^{j_1}} \cdots \frac{\partial \bar{x}^{i_n}}{\partial x^{j_n}} \frac{\partial x^{j_{n+1}}}{\partial \bar{x}^{i_{n+1}}} \cdots \frac{\partial x^{j_m}}{\partial \bar{x}^{i_m}} T^{j_1\dots j_n}_{j_{n+1}\dots j_m}(x_1,\ldots,x_k).$

so, according to this, the upper indice seems to indicate contravariant and the lower indice seems to indicate covariant.

However, according to http://en.wikipedia.org/wiki/Tensor#As_multilinear_maps,

$T^{i_1\dots i_n}_{j_1\dots j_m} \equiv T(\mathbf{\varepsilon}^{i_1},\ldots,\mathbf{\varepsilon}^{i_n},\mathbf{e}_{j_1},\ldots,\mathbf{e}_{j_m})$

This seems to indicate the upper indice of tensor refers to covariant, while the lower indice indicates contravariant.

What is wrong with my knowledge?

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    The main thing that is wrong is that the singular version of "indices" is "index". As for your question, I suppose it is possible that sources differ. From a Schaum's outline that happened to be on my desk, upper indices are contravariant ones.2012-06-27

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