BUILT-IN MATHEMATICA SYMBOL

# TensorSymmetry

TensorSymmetry[tensor]
gives the symmetry of tensor under permutations of its slots.

TensorSymmetry[tensor, slots]
gives the symmetry under permutation of the specified list of slots.

## Details and OptionsDetails and Options

• TensorSymmetry accepts any type of tensor, either symbolic or explicit, including any type of array.
• A general symmetry is specified by a generating set of pairs , where perm is a permutation of the slots of the tensor, and is a root of unity. Each pair represents a symmetry of the tensor of the form TensorTranspose[tensor, perm]==tensor.
• Some symmetry specifications have names:
•  Symmetric[{s1,...,sn}] full symmetry in the slots Antisymmetric[{s1,...,sn}] antisymmetry in the slots ZeroSymmetric[{s1,...,sn}] symmetry of a zero tensor

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

A symmetric matrix:

 Out[1]=

An antisymmetric matrix:

 Out[2]=

A symmetric array of rank 3:

 Out[2]=