IEVref: 102-03-43 ID: Language: en Status: Standard Term: antisymmetric tensor Synonym1: Synonym2: Synonym3: Symbol: Definition: tensor of the second order defined by a bilinear form such that $f\left(U\text{,}\text{\hspace{0.17em}}V\right)=-f\left(V\text{,}\text{\hspace{0.17em}}U\right)$Note 1 to entry: The components of an antisymmetric tensor are such that ${T}_{ij}=-{T}_{ji}$, and in particular ${T}_{ii}=0$. Note 2 to entry: An antisymmetric tensor defined on a three-dimensional space has three strict components which can be considered as the coordinates ${W}_{1}\text{,}{W}_{2}\text{,}{W}_{3}$ of an axial vector: $\left(\begin{array}{ccc}0& {W}_{3}& -{W}_{2}\\ -{W}_{3}& 0& {W}_{1}\\ {W}_{2}& -{W}_{1}& 0\end{array}\right)$ The axial vector associated with the antisymmetric tensor $U\otimes V-V\otimes U$ is the vector product of the two vectors. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: