2008/01/18 by Stephen J. Sangwine, Sangwine, Stephen J.
Computer Science · Mathematics · Physics and Astronomy · #11R52 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:11R52
paper · pdf · doi:10.48550/arxiv.0801.2887
4 pages
arxiv created 2008/01/18 · openalex publication_date 2008/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown that any such function may be represented using at most four quaternion coefficients. In this paper, a new and simple method is presented for obtaining these coefficients numerically using a matrix approach which also gives an alternative proof of the canonic forms.