Antisymmetric

Antisymmetric[{s1,,sn}]

represents the symmetry of a tensor that is antisymmetric in the slots si.

Details

  • The slots si 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.

Examples

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Basic Examples  (2)

This matrix is antisymmetric:

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Out[1]=

Declare a rank-4 array to be antisymmetric in three slots:

In[1]:=
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Then any transposition involving those slots is equivalent to the original tensor, perhaps up to a sign:

In[2]:=
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Out[2]=

Scope  (3)

Applications  (3)

Properties & Relations  (3)

Possible Issues  (1)

See Also

Symmetric  TensorSymmetry  TensorTranspose  Arrays  Matrices

Tutorials

Introduced in 2012
(9.0)