A 3x3 rotation matrix is given. We know the properties of rotation matrix:
- The columns of rotation matrix are unit vectors perpendicular to each other.
- The column vectors indicate where the unit vectors along the principal axes are transformed.
- The rows of rotation matrix are unit vectors perpendicular to each other.
- The row vectors indicate the vectors that are transformed into the unit vectors along the principal axes.
- The inverse of rotation matrix is its transpose.
Suppose, we don't know anything about the Rodrigues formula, so we can't use Trace(R) = 1+2cos$\theta$. Is it possible to find the axis and angle of rotation from the given rotation matrix and the properties of rotation matrix? I need an answer with proper explanation.