NOTE 1 The bilinear form can be represented by $f\left(X,Y\right)=\left({\displaystyle \sum _i{U}_i{X}_i}\right)\left({\displaystyle \sum _j{V}_j{Y}_j}\right)={\displaystyle \sum _{ij}{U}_i}{V}_j{X}_i{Y}_j$ 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 The dyadic product of two vectors is denoted by $U\otimes V$ or $UV$.