View source for Symmetric tensor

''with respect to a pair of indices''

A tensor which is invariant under transposition of this pair of indices. The result of [[Alternation|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)|Symmetrization (of tensors)]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  L. Brand,   "Vector and tensor analysis" , Wiley  (1947)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  E. Nelson,   "Tensor analysis" , Princeton Univ. Press  (1967)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  B. Spain,   "Tensor calculus" , Oliver &amp; Boyd  (1953)</TD></TR></table>