Explain me how to get rotation axis from rotation matrix? Please?

Something like this I think... If the rotation matrix is A, and v is the vector corresponding to the axis of rotation, then: Av = v because applying a rotation to v doesn’t change it. This is an eigenvalue equation with the eigenvalue = 1 You have to find the eigenvector. I guess after doing the working it will come to: (1, 0, 1) This has magnitude = √(1² + 0² + 1²) = √2 so the normalised eigenvector is: (1/√2)(1, 0, 1) = (1/√2, 0,-1/√2) Since the axis of rotation could point in the opposite direction we could multiply this by -1 (reverses direction) giving (-1/√2, 0,1/√2) as an alternative.

Quote "You have to find the eigenvector. I guess after doing the working it will come to: (1, 0, 1) " Could you please show this working to me as i have no idea how to solve "Av=v". I'm reading 'Mathematical methods in the physical sciences' by Mary L .Boas. On page 129, Ex 5 it doesn't explain whatsoever how to solve Gr=r so I basically have NO IDEA how to find the axis of rotation. Somebody P.L.E.A.S.E help me, I am so frustrated with this. Any input will be SO appreciated.