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?
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?
No, but it is certainly antisymmetric. consider the two 1-tensors, $\partial_i$, and $A_j$, then look at $F_{ij}=\partial_i A_j - \partial_j A_i$. This has zero components, but they are not all zero... Maybe go through them component by component until that's clear :)