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Dyad

Dyads extend vectors to provide an alternative description to second tensor rank tensors. A dyad D(A,B) of a pair of vectors A and B is defined by D(A,B)=AB. The dot product is defined by

A·BC=(A·B)C
(1)
AB·C=A(B·C),
(2)

and the colon product by

AB:CD=C·AB·D=(A·C)(B·D).
(3)

See also

Dyadic, Tensor

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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.

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Dyad

Cite this as:

Weisstein, Eric W. "Dyad." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Dyad.html

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