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Factorization of Affinities

Published online by Cambridge University Press:  20 November 2018

Erich W. Ellers
Erich W. Ellers*
Affiliation:
University of Toronto, Toronto, Ontario
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The decomposition of mappings into a minimal number of simple mappings is a common sight in geometry. One well-known instance is the representation of a plane motion by three reflections (see e.g. H. S M. Coxeter [3]) or the representation of equiaffinities by a minimal number of shears or reflections ([14], [5], [7], [8]). Theorems of this nature not only give valuable insight into the nature of the mapping, but they are also often used as a base for characterization theories (see e.g. F. Bachmann [2], M. Götzky [10]). A more abstract version of the same type of results is the famous Cartan-Dieudonné theorem. Its usefulness is indisputable. P. Scherk [13] gave a refined version of this theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 354 - 362
Copyright
Copyright © Canadian Mathematical Society 1979

References

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