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by msla
2957 days ago
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> So a rotation would have no eigenvectors because none of the points move in a straight line, while a scaling along the x axis would have an eigenset that was also along the x axis, consisting of the points that were moved straight up or down. Maybe I'm being pedantic, but rotation matrices have eigenvectors and eigenvalues, but the eigenvalues are imaginary because imaginary numbers are rotations in the complex plane. It's exactly like saying x^2 = -1 has no solutions: It has two solutions, like any other quadratic, but neither of them are real. In three dimensions, rotation matrices have three eigenvalues, one of them being 1, and the eigenvector corresponding to that eigenvalue is, naturally, the rotation axis. https://en.wikipedia.org/wiki/Rotation_matrix |
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