🔄Complex numbers are limited to describing 2D rotations due to commutative multiplication, while 3D rotations do not commute.
🔄Matrix exponentials provide a way to represent rotations in higher dimensions, allowing for non-commutative multiplication.
🔄Matrix exponentials can be visualized as defining a velocity vector field that describes the movement of points in space.
🔄Applying a matrix exponential to a point results in its position after a certain time of flowing along the velocity field.
🔄The matrix exponential for a 3D rotation can be computed by plugging a scaled rotation matrix into the exponential function.