Quaternion Matrices

João Pedro Morais, Svetlin Georgiev and Wolfgang Sprößig
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João Pedro Morais: University of Aveiro, CIDMA
Svetlin Georgiev: University of Sofia St Kliment Ohridski Faculty of Mathematics and Informatics, Department of Differential Equations
Wolfgang Sprößig: TU Bergakademie Freiberg, Institut für Angewandte Analysis

Chapter 9 in Real Quaternionic Calculus Handbook, 2014, pp 133-147 from Springer

Abstract: Abstract In a brief outline, the next portion of text describes a way of representing quaternion matrices in such a way that quaternionic addition and multiplication correspond to matrix addition, (scalar) matrix multiplication, and matrix transposition. Besides the discussion of the quaternionic analogues to complex matrices, we will also discuss the possibility of decomposing quaternions with respect to well known matrix decompositions, which are related to solving systems of linear equations. Even though it is self-contained, the reader will comprehend the necessity of this notions while pursuing the subject. Our presentation is organized in such a way that the analogies between quaternion, noncommutativity, and quaternion matrix, on one hand, and determinant, rank, and eigenvalues, on the other, are mastered. The relations between these concepts will come into view more clearly through the text, motivating our insight to the problem.

Keywords: Quaternion Matrix; Quaternary Additions; Quaternary Analogue; Quaternion Entries; Quaternion Square (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0622-0_9

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DOI: 10.1007/978-3-0348-0622-0_9

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