ABSTRACT
Quaternions were introduced by Sir William Rowan Hamilton in the middle of the nineteenth century, at a time when vector analysis did not exist. A quaternion is a hypercomplex 4D number of the form: w + xi + yj + zk. There are rules for quaternion multiplication, inversion, and normalization. Quaternions can effectively represent spatial rotations, by applying them to 3D vectors or when converted into 3 × 3 rotation matrices.
