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A tensor exercise in a text reads: If $T_i$ are the components of a covariant vector $T$, show that $S_{ij}:=T_iT_j-T_jT_i$ is an order 2 covariant tensor $S$.

Am I missing something or is $S$ uniformly zero?

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    Dear student: it would be helpful if you made explicit what text this is, as the source can make it easier to make sense of it (the tiny detail of whether this is a text intended for mathematicians or physicists would already be a useful piece of information!)2012-01-13

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