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Using Quaternion-Valued Linear Algebra

2013/11/29 by Dominik Schulz, Schulz, Dominik, Reiner S. Thomä +1
Mathematics · #17B40 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B40

paper · pdf · doi:10.48550/arxiv.1311.7488

1st revision: - Section 3.1: added details on the two different kinds of ordering in matrix products - Section 5: added details on the relation of the left/right inverse - Section 5: added details on the complex inverse - Typos corrected - Minor formulation changes - Acknowledgement section added

arxiv created 2014/03/20 · arxiv updated 2014/03/21

Abstract

Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear algebra over skew fields. To this end, we discuss ways of notation that account for the non-commutativity of the quaternion multiplication.

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