Matrix Representation of Dual Quaternions

Abstract

After a review of some properties of dual quaternions, De Moivre's and Euler's formulas for the matrices associated with these quaternions are studied. In special case, De Moivre's formula implies that there are uncountably many matrices of unit dual quaternions satisfying 4 n A I = for n≥3. Also; we give the relation between the powers of matrices of dual quaternions.