The Exponential of a Quaternionic Matrix

The exponential map is important because it provides a map from the Lie algebra of a Lie group into the group itself. We focus on matrix groups over the quaternions and the exponential map from their Lie algebras into the groups. Since quaternionic multiplication is not commutative, the process of calculating the exponential of a matrix over the quaternions is more involved than the process of calculating the exponential of a matrix over the real or complex numbers. We develop processes by which this calculation may be reduced to a simpler problem, and provide some examples. Acknowledgements: This project was made possible by a research grant from the Undergraduate Research Office and the Honors Program at the University of Nevada, Reno. I am also indebted to my mentor, Dr. Valentin Deaconu, for his expertise and support throughout the process of writing this paper. Page 30 RHIT Undergrad. Math. J., Vol. 12, No. 2