A second-tensor rank symmetric tensor is defined as a tensor A for which A^(m n) = A^(n m). Any tensor can be written as a sum of symmetric and antisymmetric parts A^(m n) | = | 1/2(A^(m n) + A^(n m)) + 1/2(A^(m n) - A^(n m)) | = | 1/2((B_S)^(m n) + (B_A)^(m n)). The symmetric part of a tensor is denoted using parentheses as T_(a, b) congruent 1/2(T_(a b) + T_(b a)) T_(a_1, a_2, ..., a_n) congruent 1/(n!) sum_permutations T_(a_1 a_2 ...a_n).

antisymmetric tensor | tensor