Mathematica
BUILT-IN MATHEMATICA SYMBOL

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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Out[1]=

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

In[1]:=
Click for copyable input

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)Scope (3)

Applications (3)Applications (3)

Properties & Relations (3)Properties & Relations (3)

Possible Issues (1)Possible Issues (1)

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