Antisymmetric

Antisymmetric[{s1, ..., sn}]
represents the symmetry of a tensor that is antisymmetric in the slots .

DetailsDetails

  • The slots must be different positive numbers. The order of the list is irrelevant.
  • Antisymmetric[{}] and Antisymmetric[{s}] are both equivalent to the identity symmetry.
  • Antisymmetric[All] represents the symmetry of a tensor that is antisymmetric in all its slots.
  • If an array is antisymmetric in a set of slots, then all those slots have the same dimensions.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

This matrix is antisymmetric:

In[1]:=
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Declare a rank-4 array to be antisymmetric in three slots:

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Then any transposition involving those slots is equivalent to the original tensor, perhaps up to a sign:

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Out[2]=
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