Characterizing isoclinic matrices and the Cayley Factorization

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • University of Bath

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 44 matrix to be expressed as the product of two isoclinic matrices and this is a the 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.

Details

Original languageEnglish
JournalInstitution of Mechanical Engineers. Proceedings. Part G: Journal of Aerospace Engineering
Early online date28 Oct 2015
Publication statusPublished - 2015

Keywords

  • Quaternion, double quaternion, dual quaternion, Cayley factorization, rigid-body transform