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Abstract
Quaternions, particularly the double and dual forms, are important for the representation rotations and more general rigidbody motions. The Cayley factorization allows a real orthogonal 4 × 4 matrix to be expressed as the product of two isoclinic matrices and this is a key part of the underlying theory and a useful tool in applications. An isoclinic matrix is defined in terms of its representation of a rotation in fourdimensional space. This paper looks at characterizing such a matrix as the sum of a skew symmetric matrix and a scalar multiple of the identity whose product with its own transpose is diagonal. This removes the need to deal with its geometric properties and provides a means for showing the existence of the Cayley factorization.
Original language  English 

Pages (fromto)  32673273 
Journal  Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 
Volume  230 
Issue number  18 
Early online date  28 Oct 2015 
DOIs  
Publication status  Published  Nov 2016 
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Dive into the research topics of 'Characterizing isoclinic matrices and the Cayley factorization'. Together they form a unique fingerprint.Projects
 1 Finished

Algebraic Modelling of 5axis Tool Path Motions
Engineering and Physical Sciences Research Council
31/03/14 → 30/03/17
Project: Research council