# symmetric tensor

Let $V$ be a vector space^{} over a field. Let ${S}_{n}$ be the symmetric group^{} on
$\{1,\mathrm{\dots},n\}$. An order-n tensor (http://planetmath.org/TensorProduct) $A\in {V}^{\otimes n}$ is said to
be if $P(\sigma )A=A$ for all $\sigma \in {S}_{n}$,
where $P(\sigma )$ is the permutation operator associated to $\sigma $.
The set of symmetric tensors in ${V}^{\otimes n}$ is denoted by
${S}^{n}(V)$.

Title | symmetric tensor |
---|---|

Canonical name | SymmetricTensor |

Date of creation | 2013-03-22 16:15:41 |

Last modified on | 2013-03-22 16:15:41 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 5 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 15A03 |