Dual Quaternions and Dual Quaternion Vectors

We introduce a total order and an absolute value function for dual numbers. The absolute value function of dual numbers takes dual number values, and has properties similar to those of the absolute value function of real numbers. We define the magnitude of a dual quaternion, as a dual number. Based upon these, we extend 1-norm, $$\infty$$ -norm, and 2-norm to dual quaternion vectors.