Characterizing isoclinic matrices and the Cayley Factorization

Robert Cripps, Glen Mullineux, Benjamin Cross, Matthew Hunt

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


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


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