The Exponential of a Quaternionic Matrix

Authors

Casey Machen, University of Nevada, RenoFollow

Abstract

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.

Author Bio

Casey Machen is currently a Ph.D. student at Michigan State University. He graduated from the University of Nevada, Reno in 2011 where he received a B.S. in Mathematics. He worked under Professor Valentin Deaconu at UNR and received an Honors Undergraduate Research Award his senior year for this project.

Faculty Sponsor

Valentin Deaconu

Recommended Citation

Machen, Casey (2011) "The Exponential of a Quaternionic Matrix," Rose-Hulman Undergraduate Mathematics Journal: Vol. 12: Iss. 2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol12/iss2/3