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Symmetric tensor

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with respect to a pair of indices

A tensor which is invariant under transposition of this pair of indices. The result of alternation of a symmetric tensor with respect to this pair of indices is zero. A tensor is symmetric with respect to a set of indices if it is symmetric with respect to any two indices from this set.


Comments

Cf. also Symmetrization (of tensors).

References

[a1] L. Brand, "Vector and tensor analysis" , Wiley (1947)
[a2] E. Nelson, "Tensor analysis" , Princeton Univ. Press (1967)
[a3] B. Spain, "Tensor calculus" , Oliver & Boyd (1953)
How to Cite This Entry:
Symmetric tensor. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Symmetric_tensor&oldid=14611
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098