It was pretty cool to stumble upon Euler's formula as the eigenvalues of the rotation matrix.
det(Rot  kI) = (cos t  k)^{2} + sin^{2}t
=k^{2}2(cos t)k + cos^{2}t + sin^{2}t
=k^{2}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.
