Loterre: Mathematics: antisymmetric tensor

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antisymmetric tensor

In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged. The index subset must generally either be all covariant or all contravariant.
For example,
${\\displaystyle T_{ijk\\dots }=-T_{jik\\dots }=T_{jki\\dots }=-T_{kji\\dots }=T_{kij\\dots }=-T_{ikj\\dots }}$
holds when the tensor is antisymmetric with respect to its first three indices.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Antisymmetric_tensor)

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