Content deleted Content added
m →Definition: Minor Clean Up and Fixes, typo(s) fixed: … → ... |
Zirconcode (talk | contribs) m clarified what V stands for |
||
Line 7:
:<math>T_{i_1i_2\cdots i_r} = T_{i_{\sigma 1}i_{\sigma 2}\cdots i_{\sigma r}}.</math>
The space of symmetric tensors of order ''r'' on a finite-dimensional [[vector space]] ''V'' is [[natural isomorphism|naturally isomorphic]] to the dual of the space of [[homogeneous polynomial]]s of degree ''r'' on ''V''. Over [[field (mathematics)|fields]] of [[characteristic zero]], the [[graded vector space]] of all symmetric tensors can be naturally identified with the [[symmetric algebra]] on ''V''. A related concept is that of the [[antisymmetric tensor]] or [[alternating form]]. Symmetric tensors occur widely in [[engineering]], [[physics]] and [[mathematics]].
==Definition==
| |||