Characterizing isoclinic matrices and the Cayley factorization. (November 2016)

• Record Type: Journal Article
• Authors: Hunt, Matthew; Mullineux, Glen; Cripps, Robert J; Cross, Ben
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 230:Number 18(2016)
• Page Start: 3267
• Page End: 3273
• Publication Date: 2016-11
• Subjects: Quaternion -- double quaternion -- dual quaternion -- Cayley factorization -- rigid-body transform; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/0954406215609943
• Languages: English
• ISSNs: 0954-4062

Abstract

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.