E.M.S. Hitzer

*(Nat. Symp. on Math. Sc., 2001.3, Nagpur, India.) Proc. Einst. Foundation Int.* **1**, 1-26 (2001.4), Nagpur, India.

**Abstract:**
This paper first reviews how anti-symmetric matrices in two dimensions
yield imaginary eigenvalues and complex eigenvectors. It is shown how
this carries on to rotations by means of the Cayley transformation.
Then the necessary tools from real geometric algebra are introduced
and a real geometric interpretation is given to the eigenvalues and
eigenvectors. The latter are seen to be two component eigenspinors
which can be further reduced to underlying vector duplets. The eigenvalues
are interpreted as rotors, which rotate the underlying vector duplets.
The second part of this paper extends and generalizes the treatment to
three dimensions. The final part shows how all entities and relations
can be obtained in a constructive way, purely assuming the geometric
algebras of 2-space and 3-space.

[Postscript] 296k, gzip compressed

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