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Eigenvectors of the \(\mathrm{SO}(3,\mathbb{R})\) matrices. (English) Zbl 1429.15007

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

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B10 Orthogonal matrices
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