represents the domain of arrays of rank r and dimensions di.


represents the domain of arrays of dimensions di, with components in the domain dom.


represents the subdomain of arrays with dimensions di and symmetry sym.


  • The length r of the list of dimensions is the rank or depth of the arrays in the domain.
  • Valid dimension specifications di in Arrays[{d1,,dr},dom,sym] are positive integers. It is also possible to work with symbolic dimension specifications.
  • Valid component domain specifications dom are either Reals or Complexes. Arrays[{d1,,dr}] uses Complexes by default.
  • The symmetry sym can be given in several forms. First, it can be given as expressions like Symmetric[{s1,,sk}] or Antisymmetric[{si,,sk}], with the slots si being different positive integers between 1 and the rank r. It can also be given as a list of generators of the form {perm,ϕ}, representing that the array stays invariant under simultaneous transposition by the permutation perm and multiplication by the root of unity ϕ. In addition, it can be given as the internal direct product {sym1, sym2,} of those forms.
  • When the symmetry is not specified, then none is assumed. The absence of symmetry, or identity symmetry, is represented by an empty list {} of generators.


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Basic Examples  (1)

A fully symmetric real array of rank 3 in dimension 4:

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Any transposition is equivalent to the original array:

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Scope  (2)

Applications  (3)

Properties & Relations  (3)

Possible Issues  (2)

Introduced in 2012