2005/06/02 by Todd A. Ell, Stephen J. Sangwine · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Mathematics and Applications #math.RA #msc:11R52
paper · pdf · doi:10.1016/j.camwa.2006.10.029
published as Computers and Mathematics with Applications, 53, (1), January 2007, 137-143
arxiv created 2005/06/02 · openalex publication_date 2007/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of involutions. We show that the conjugate of a quaternion may be expressed using three mutually perpendicular involutions. We also show that any set of three mutually perpendicular quaternion involutions is closed under composition. Finally, we show that projection of a vector or quaternion can be expressed concisely using involutions.