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tickle_monste
tickle_monste is offline
#1
Dec15-09, 10:41 PM
P: 70
It was pretty cool to stumble upon Euler's formula as the eigenvalues of the rotation matrix.

det(Rot - kI) = (cos t - k)2 + sin2t
=k2-2(cos t)k + cos2t + sin2t
=k2-2(cos t)k + 1

k = {2cos t +/- [tex]\sqrt{4cos^2(t) - 4}[/tex]}/2
k = cos t +/- [tex]\sqrt{cos^2(t) - 1}[/tex]
k = cos t +/- [tex]\sqrt{cos^2(t) - cos^2t - sin^2(t)}[/tex]
k = cos t +/- [tex]\sqrt{-sin^2(t)}[/tex]
k = cos t +/- i sin t = e(+/-)it

I was wondering what the eigenvalues are for the rotation matrix in 3D, and if there's a 3D equivalent to Euler's formula.
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