Title: The decomposition of an orthogonal transformation as a product of reflections
Abstract: In this work, an algorithm to decompose a given orthogonal transformation as a product of reflections through hyperplanes is presented. This in fact constitutes a constructive proof of a Cartan theorem, valid over any field K=Q, R or C. Clifford algebras are used to explicitly calculate the reflections that decompose a given orthogonal transformation. Our algorithm may have application in fields such as computer graphics or crystallography, and can also play an important role in orthogonal elimination and the solution of equations systems. An explicit example is provided and we apply our results to the crystallographic problem of coincidence lattices.
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 15
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