Symmetric tensor: Difference between revisions

Revision as of 01:22, 27 February 2016

Revision as of 01:22, 27 February 2016

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:<math>T = T_{i_1i_2\cdots i_k}e^{i_1}\otimes e^{i_2}\otimes\cdots \otimes e^{i_k},</math>

then

:<math>\operatorname{Sym}\, T = \frac{1}{k!}\sum_{\sigma\in \mathfrak{S}_k} T_{i_{\sigma 1}i_{\sigma 2}\dotscdots i_{\sigma k}} e^{i_1}\otimes e^{i_2}\otimes\cdots \otimes e^{i_k}.</math>

The components of the tensor appearing on the right are often denoted by