gives the signature of the permutation needed to place the elements of list in canonical order.


  • The signature of the permutation is (-1)n, where n is the number of transpositions of pairs of elements that must be composed to build up the permutation.
  • If any two elements of list are the same, Signature[list] gives 0.
  • Signature can be used on expressions with any head, not only List.


open allclose all

Basic Examples  (1)

Applications  (3)

Find even permutations:

Rank-3 totally antisymmetric (Levi-Civita) tensor:

Contractions of Levi-Civita tensors:

Properties & Relations  (2)

Find components of a 3D cross product:

Compute a determinant:

Compare with builtin Det:

Possible Issues  (2)

The precision of a number influences its ordering:

Signature evaluates even for symbolic arguments:

Use Unevaluated to insert an unevaluated Signature:

Use Signature directly inside Table:

Neat Examples  (1)

Introduced in 1988