Symmetric versus Antisymmetric Tensors
Swap indices, or equivalently for rank-2 tensors, transpose the matrix.
Symmetric tensor: no sign or value changes after transposing.
-
Antisymmetric tensor: all entries change signs but not value after transposing. -
Asymmetric tensor has no simple pattern after transposing.
Any asymmetric tensor can be represented by a symmetric tensor (averaged values of 2 indicies) and an antisymmetric tensor (+ and - diviations from average).
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