IEVref: 102-03-41 ID: Language: en Status: Standard Term: dyadic product Synonym1: tensor product, Synonym2: Synonym3: Symbol: Definition: for two vectors U and V in an n-dimensional Euclidean space, tensor of the second order defined by the bilinear form $f\left(X\text{,}\text{\hspace{0.17em}}Y\right)=\left(U\cdot X\right)\left(V\cdot Y\right)$, where X and Y are any vectors in the same spaceNote 1 to entry: The bilinear form can be represented by $f\left(X,Y\right)=\left(\sum _{i}{U}_{i}{X}_{i}\right)\left(\sum _{j}{V}_{j}{Y}_{j}\right)=\sum _{ij}{U}_{i}{V}_{j}{X}_{i}{Y}_{j}$ in terms of the coordinates of the vectors. The dyadic product is then the tensor with components ${T}_{ij}={U}_{i}{V}_{j}$. Note 2 to entry: The dyadic product of two vectors is denoted by $U\otimes V$ or $UV$. 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: