Finding direction of rotation I'm given matrix $A$ that represents a rotation. I can find the axis of rotation by solving $Av=v$. I can then determine the angle of rotation by taking $u$ such that $u\perp v$ and then computing $\theta$ via $u\cdot Au=|u||Au|cos(\theta).$ How do I then determine whether the rotation is clockwise or anti-clockwise?

The sign of the shortest angle (which is in $(-\pi,\pi)$) is that of the triple product $v\cdot(u\times Au)$. (The cross product is a vector parallel to the axis, with the same or opposite orientation.)