Eigenvector of a matrix in $SO_3(\mathbb{R})$

Amol Sasane; Victor Ufnarovski

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arXiv · 1905.07404

Eigenvector of a matrix in $SO_3(\mathbb{R})$

Amol Sasane·Victor Ufnarovski

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Abstract

Let $A=[a_{ij}]\in O_3(\mathbb{R})$. We give several different proofs of the fact that the vector $$ V:=\left[\begin{array}{ccc} \displaystyle \frac{1}{a_{23}+a_{32}} & \displaystyle \frac{1}{a_{13}+a_{31}} & \displaystyle \frac{1}{a_{12}+a_{21}} \end{array}\right]^T, $$ if it exists, is an eigenvector of $A$ corresponding to the eigenvalue $1$.

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Amol Sasane, Victor Ufnarovski. 2019-05-17. Eigenvector of a matrix in $SO_3(\mathbb{R})$. https://arxiv.org/abs/1905.07404

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