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## Main Question or Discussion Point

It was pretty cool to stumble upon Euler's formula as the eigenvalues of the rotation matrix.

det(Rot - kI) = (cos t - k)

=k

=k

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

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

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 + 1k = {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.