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2015 On Reflections and Rotations in Minkowski 3-Space of Physical Phenomena
Melek Erdoğdu, Mustafa Özdemir
J. Geom. Symmetry Phys. 39: 1-16 (2015). DOI: 10.7546/jgsp-39-2015-1-16

Abstract

In this paper, we investigate the reflections in Minkowski three-space by three different approaches. Firstly, we define Lorentzian reflections with Lorentzian inner product. Then, we examine Lorentzian reflections in view of Lorentzian Householder matrices. Finally, we use pure split quaternions to derive Lorentzian reflections. For each case, we find the matrix representation of Lorentzian reflections and characterize the plane of reflection by using this matrix representation. Moreover, we prove that any Lorentzian orthogonal transformation can be represented by the composition of at most six reflections.

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Melek Erdoğdu. Mustafa Özdemir. "On Reflections and Rotations in Minkowski 3-Space of Physical Phenomena." J. Geom. Symmetry Phys. 39 1 - 16, 2015. https://doi.org/10.7546/jgsp-39-2015-1-16

Information

Published: 2015
First available in Project Euclid: 27 May 2017

zbMATH: 1337.53036
MathSciNet: MR3444882
Digital Object Identifier: 10.7546/jgsp-39-2015-1-16

Rights: Copyright © 2015 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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