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PRODUCTS OF ROTATIONS BY A GIVEN ANGLE IN THE ORTHOGONAL GROUP

Part of: Metric geometry Analytic and descriptive geometry Basic linear algebra

Published online by Cambridge University Press:  02 November 2017

M. G. MAHMOUDI Open the ORCID record for M. G. MAHMOUDI [Opens in a new window]
M. G. MAHMOUDI*
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, PO Box 11155-9415, Tehran, Iran email mmahmoudi@sharif.ir
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Abstract

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For every rotation $\unicode[STIX]{x1D70C}$ of the Euclidean space $\mathbb{R}^{n}$ ($n\geq 3$), we find an upper bound for the number $r$ such that $\unicode[STIX]{x1D70C}$ is a product of $r$ rotations by an angle $\unicode[STIX]{x1D6FC}$ ($0<\unicode[STIX]{x1D6FC}\leq \unicode[STIX]{x1D70B}$). We also find an upper bound for the number $r$ such that $\unicode[STIX]{x1D70C}$ can be written as a product of $r$ full rotations by an angle $\unicode[STIX]{x1D6FC}$.

Keywords

rotation groupreflection

MSC classification

Primary: 51F25: Orthogonal and unitary groups
Secondary: 15A23: Factorization of matrices 51N30: Geometry of classical groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 308 - 312
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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