Totally antisymmetric tensor
= Totally antisymmetric tensor
A tensor changes sign whenever two indices are interchanged. In three dimensions, a rank-two antisymmetric tensor is $A_{ij}=a_k\epsilon_{kij}$, a rank-three one is $A_{ijk}=a\epsilon_{ijk}$, and every totally antisymmetric tensor of rank greater than three vanishes.