# symmetric tensor

Let $V$ be a vector space over a field. Let $S_{n}$ be the symmetric group on $\{1,\ldots,n\}$. 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 SymmetricTensor 2013-03-22 16:15:41 2013-03-22 16:15:41 Mathprof (13753) Mathprof (13753) 5 Mathprof (13753) Definition msc 15A03