Characterizing isoclinic matrices and the Cayley factorization

Matthew Hunt, Glen Mullineux, Robert J. Cripps, Ben Cross

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)3267-3273
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume230
Issue number18
Early online date28 Oct 2015
DOIs
Publication statusPublished - Nov 2016

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