Consider a time increment of 
. The relative motion of a particle B
to A has
.
which can be writen as
In tensor notation
where the first term 
presents the strain tensor and the second term 
presents
the rotational tensor.
Note that
and
strain tensor is symmetric, the rotational tensor is antisymmetric. Example:
Deformation:
For 
the average deformation is
rate of strain
Rotation:
For the average rotation is
Rate of rotation
Experience found that fluid in pure rotation does not have stress 