Symmetric tensor: Difference between revisions

Revision as of 00:42, 12 September 2018

Revision as of 01:15, 25 February 2019

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{{Use American English|date = February 2019}}

{{Short description|tensor invariant under permutations of vectors it acts on}}

In [[mathematics]], a '''symmetric tensor''' is a [[tensor]] that is invariant under a [[permutation]] of its vector arguments:

:<math>T(v_1,v_2,\ldots,v_r) = T(v_{\sigma 1},v_{\sigma 2},\ldots,v_{\sigma r})</math>

for every permutation ''&sigma;'' of the symbols {{nowrap|{1, 2, ..., ''r''}.}} Alternatively, a symmetric tensor of order ''r'' represented in coordinates as a quantity with ''r'' indices satisfies

Alternatively, a symmetric tensor of order ''r'' represented in coordinates as a quantity with ''r'' indices satisfies

:<math>T_{i_1i_2\cdots i_r} = T_{i_{\sigma 1}i_{\sigma 2}\cdots i_{\sigma r}}.</math>