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A Decomposition of Orthogonal Transformations

Published online by Cambridge University Press:  20 November 2018

María J. Wonenburger
María J. Wonenburger*
Affiliation:
University of Toronto
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The purpose of the present note is to give a partial answer to a question raised by Professor Coxeter, namely, if an orthogonal transformation is expressed as a product of orthogonal involutions, how many involutions do we need? Our answer is partial because we are going to consider only non-degenerate symmetric bilinear forms of index 0 and fields of characteristic ≠2. Under these conditions we prove that any orthogonal transformation is the product of at most two orthogonal involutions, which implies that we can write any orthogonal transformation as the product of two involutions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 379 - 383
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Artin, E., Geometric Algebra, Interscience, New York, (1957).Google Scholar
2. Dieudonné, J., La géométrie des groupes classiques, Springer Berlin,(1955).Google Scholar