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geometry > differential geometry > tensor > symmetric tensor

algebra > multilinear algebra > tensor > symmetric tensor

Preferred term

symmetric tensor

Definition(s)

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

${\\displaystyle T(v_{1},v_{2},\\ldots ,v_{r})=T(v_{\\sigma 1},v_{\\sigma 2},\\ldots ,v_{\\sigma r})}$

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

${\\displaystyle T_{i_{1}i_{2}\\cdots i_{r}}=T_{i_{\\sigma 1}i_{\\sigma 2}\\cdots i_{\\sigma r}}.}$

Broader concept(s)

tensor

Related concept(s)

Voigt notation

In other languages

tenseur symétrique

French

URI

http://data.loterre.fr/ark:/67375/PSR-F16NMHR3-3

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