A dyadic, also known as a vector direct product, is a linear polynomial of dyads AB+CD+... consisting of nine components A_(ij) which transform as


Dyadics are often represented by Gothic capital letters. The use of dyadics is nearly archaic since tensors perform the same function but are notationally simpler.

A unit dyadic is also called the idemfactor and is defined such that


In Cartesian coordinates,


and in spherical coordinates

 I=del r.

See also

Dyad, Tensor, Tetradic, Vector Direct Product

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Arfken, G. "Dyadics." §3.5 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 137-140, 1985.Jeffreys, H. and Jeffreys, B. S. "Dyadic Notation." §3.04 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 89, 1988.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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Cite this as:

Weisstein, Eric W. "Dyadic." From MathWorld--A Wolfram Web Resource.

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