tickle_monste

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.