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Quaternions, particularly the double and dual forms, are important for the representation rotations and more general rigid-body 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 four-dimensional 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.
|Journal||Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science|
|Early online date||28 Oct 2015|
|Publication status||Published - Nov 2016|
Hunt, M., Mullineux, G., Cripps, R. J., & Cross, B. (2016). Characterizing isoclinic matrices and the Cayley factorization. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(18), 3267-3273. https://doi.org/10.1177/0954406215609943