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.
Citation
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
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