Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
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
2  
This means that there's not an invariant vector line. –  Sami Ben Romdhane 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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.