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What does it geometrically mean for a matrix to not have an real eigenvalues? I know for rotations you do not get real eigenvalues but I think there are other cases too.

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Rotations do sometimes have real eigenvalues (of $\pm 1$ when $\theta = n\pi$ where $n\in\mathbb{Z}$). – Cameron Williams Dec 3 '13 at 18:50
Oh, this is true. So it only works for certain matrices. – The Waller Dec 3 '13 at 18:51
This means that there's not an invariant vector line. – user63181 Dec 3 '13 at 18:52
What is an invariant vector line? And how does it affect if geometrically? – The Waller Dec 3 '13 at 18:56
Do you know what the geometrical meaning is for a matrix that has least one eigenvalue? If so, negate that meaning. – Michael Hoppe Dec 3 '13 at 18:58

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