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geometrical represetation of dyadic product of two vector

a12najafi's picture


I am struggling to understand how can I explain the dyadic product between two Cartesian vectors (which should be dyadic product of a form and a vector in general).

For instance, how can I geometrically explain that the Schmid orientation tensor which is a dyadic product of the unit normal and unit tangent of a slip plane represent the slip system geometry in a crystal?





as you know the dyadic product of two vectors is a tensor , sth like a square matrix. For example  \left( \begin{array}{cc}<br />
0 & -1 \\<br />
1 & 0<br />
\end{array}<br />
\right)      which is the result of    ji-ij ,   is a 90° rotation in 2D . So here you have a tensor of second order , which represents a transformation and in  plain text: a rotation of 90° if dot-operated  on a vector in 2D. 
In the same way you can try to find what your tensor of interest does as a transformation.




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