  Formal models of opinion formation commonly represent an individual's opinion
by a value on a fixed opinion interval. We propose an alternative modeling
method wherein interpretation is only provided to the relative positions of
opinions vis-\`a-vis each other. This method is then considered in a similar
setting as the discrete-time Altafini model (an extension of the well-known
DeGroot model), but with more general influence weights. Even in a linear
framework, the model can describe, in the long run, polarization, dynamics with
a periodic pattern, and (modulus) consensus formation. In addition, in our
alternative approach key characteristics of the opinion dynamic can be derived
from real-valued square matrices of influence weights, which immediately allows
one to transfer matrix theory insights to the field of opinion formation
dynamics under more relaxed conditions than in the DeGroot or discrete-time
Altafini models. A few specific themes are covered: (i) We demonstrate how
stable patterns in relative opinion dynamics are identified which are hidden
when opinions are considered in an absolute opinion framework. (ii) For the
two-agent case, we provide an exhaustive closed-form description of the
relative opinion model's dynamic in the long run. (iii) We explore group
dynamics analytically, in particular providing a non-trivial condition under
which a subgroup's asymptotic behavior carries over to the entire population.
