E.M.S. Hitzer

To appear in C. Doran, L. Dorst and J. Lasenby eds. *Applied Geometrical Algebras in
Computer Science and Engineering, AGACSE 2001,* Birkhauser 2001.

**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
a real geometric interpretation is given to the eigenvalues and eigenvectors
by means of real geometric algebra.
The eigenvectors are seen to be *two component eigenspinors* which can be
further reduced to underlying
vector duplets. The eigenvalues are interpreted as rotation operators, which
rotate the underlying vector
duplets. The second part of this paper extends and generalizes the treatment
to three dimensions.
Finally the four-dimensional problem is stated.

[Postscript]
62k, gzip compressed

AGACSE 2001 conference poster

[Geometric Calculus Japan index]