Abstract
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical meaning as spinor couples and dyads locally describing 2D surfaces. A detailed study of algebraic relationships between the spinor sets belonging to different quaternion units is suggested as an initial step aimed at producing a self-consistent geometric image of spinor-surface distribution on the physical 3D space background.
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