High Quality Content by WIKIPEDIA articles! In mathematics, a symmetric tensor is tensor that is invariant under a permutation of its vector arguments. The space of symmetric tensors of rank r on a finite dimensional vector space is naturally isomorphic to the dual of the space homogeneous polynomials of degree r on V. Over 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.

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