It was pretty cool to stumble upon Euler's formula as the eigenvalues of the rotation matrix.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Eigenvalue of 3D rotation matrix

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