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