dyadic corresponds to second order tensor as well as 3X3 matrix. Therefore, the coefficient matrix connection forces and fluxes, which are vectorial quantities in 3D space may be represented dyadic operator. Namely J = D. F ; D= might have the following nonian form in Cartesian coordinate system: D= SUM Di k Ii Ik where Ii Ik is a operator called dyad, they are non cumuting operators.
As long as one doesn't deal with the transformation properties of the second order tensors it is more convenient to formulate the problem in dyadic format and make all the mathematical manipulation using vector algebra at the end convert to the Cartesian or curve-linear coordinates systems for the numerical computations and coding.
NOTE: Advanced Vector Analysis 'with applications to Physics'' by C. E. Weatherburn , London, G. Bell and Sons. Ltd 1954
'I purchased this book in 1955' since them it became my best friend!
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