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2019 Eigenvectors of the SO(3,${\mathbb{R}}$) Matrices
Amol Sasane, Victor Ufnarovski
J. Geom. Symmetry Phys. 53(none): 85-102 (2019). DOI: 10.7546/jgsp-53-2019-85-102

Abstract

Let $R=(r_{ij})\in$ SO(3,${\mathbb{R}}$). We give several different proofs of the fact that the vector $$ V:=\Big( \displaystyle \frac{1}{r_{23}+r_{32}}, \displaystyle \frac{1}{r_{13}+r_{31}}, \displaystyle \frac{1}{r_{12}+r_{21}}\Big)^t $$ if it exists, is an eigenvector of $R$ corresponding to the eigenvalue one.

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Amol Sasane. Victor Ufnarovski. "Eigenvectors of the SO(3,${\mathbb{R}}$) Matrices." J. Geom. Symmetry Phys. 53 85 - 102, 2019. https://doi.org/10.7546/jgsp-53-2019-85-102

Information

Published: 2019
First available in Project Euclid: 28 October 2019

zbMATH: 1429.15007
MathSciNet: MR3971650
Digital Object Identifier: 10.7546/jgsp-53-2019-85-102

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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