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> So a rotation would have no eigenvectors

Rotations have eigenvectors: a 2D rotation has two complex eigenvectors, a 3D rotation has one real and two complex eigenvectors, ...

That's a fair and true catch, but I can cover myself by pointing out that the article was only talking about matrices in R^(m x n). ;)

When your field of interest is the reals, those complex eigenvectors don't matter.