# geometrical represetation of dyadic product of two vector

Greetings,

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?

Thanks,

Ali

## Comments

### geometrical representation of dyadic product of two vectors

Hello,

as you know the dyadic product of two vectors is a tensor , sth like a square matrix. For example $\left( \begin{array}{cc}
0 & -1 \\
1 & 0
\end{array}
\right)$
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.

regards

Roozbeh