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Dyad

Dyads extend Vectors to provide an alternative description to second Rank Tensors. A dyad $D({\bf A},{\bf B})$ of a pair of Vectors ${\bf A}$ and ${\bf B}$ is defined by $D({\bf A},{\bf B}) \equiv {\bf A}{\bf B}$. The Dot Product is defined by

\begin{displaymath}
{\bf A}\cdot {\bf BC} \equiv ({\bf A}\cdot {\bf B}){\bf C}
\end{displaymath}


\begin{displaymath}
{\bf AB}\cdot {\bf C} \equiv {\bf A}({\bf B}\cdot {\bf C}),
\end{displaymath}

and the Colon Product by

\begin{displaymath}
{\bf AB}:{\bf CD} \equiv {\bf C}\cdot {\bf AB}\cdot {\bf D} = ({\bf A}\cdot{\bf C})({\bf B}\cdot {\bf D}).
\end{displaymath}


References

Morse, P. M. and Feshbach, H. ``Dyadics and Other Vector Operators.'' §1.6 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 54-92, 1953.




© 1996-9 Eric W. Weisstein
1999-05-24