In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T ( v σ 1 , v σ 2 , … , v σ r ) {\displaystyle T(v_{1},v_{2},\ldots ,v_{r})=T(v_{\sigma 1},v_{\sigma 2},\ldots ,v_{\sigma r})} for every permutation σ of the symbols {1, 2, ..., r}. Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies T i 1 i 2 ⋯ i r = T i σ 1 i σ 2 ⋯ i σ r .
In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T ( v σ 1 , v σ 2 , … , v σ r ) {\displaystyle T(v_{1},v_{2},\ldots ,v_{r})=T(v_{\sigma 1},v_{\sigma 2},\ldots ,v_{\sigma r})} for every permutation σ of the symbols {1, 2, ..., r}. Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies T i 1 i 2 ⋯ i r = T i σ 1 i σ 2 ⋯ i σ r .
Source: Wikipedia "Symmetric tensor" · CC BY-SA 4.0
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