ABSTRACT
The authors will begin their study of dual quaternions by investigating some of the unique algebra associated with dual quaternions. They shall focus, in particular, on the notions of conjugates and dot products for dual quaternions. But before they commence with their study of the algebra of dual quaternions, they provide for background, contrast, and completeness a short list of formulas from quaternion algebra that they shall need to invoke from time to time. Moreover, they can easily verify the third property, since In the quaternion algebra dot products, lengths, and angles are real numbers. But in the algebra of dual quaternions dot products, lengths, and angles are dual real numbers. To motivate the definition of the dot product for dual quaternions, they begin with a formula for the dot product of two quaternions.
