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IEVref: | 102-03-41 | ID: | |

Language: | en | Status: Standard | |

Term: | dyadic product | ||

Synonym1: | tensor product, <of two vectors> | ||

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Definition: | for two vectors and U in an Vn-dimensional Euclidean space, tensor of the second order defined by the bilinear form $f(X\text{,}\text{\hspace{0.17em}}Y)=(U\cdot X)(V\cdot Y)$, where and X are any vectors in the same spaceYNote 1 to entry: 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 to entry: The dyadic product of two vectors is denoted by $U\otimes V$ or $UV$. | ||

Publication date: | 2008-08 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO | ||

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Note 1 to entry: 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 to entry: The dyadic product of two vectors is denoted by $U\otimes V$ or $UV$.