Projects per year

### 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 language | English |
---|---|

Pages (from-to) | 3267-3273 |

Journal | Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |

Volume | 230 |

Issue number | 18 |

Early online date | 28 Oct 2015 |

DOIs | |

Publication status | Published - Nov 2016 |

## Fingerprint Dive into the research topics of 'Characterizing isoclinic matrices and the Cayley factorization'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Algebraic Modelling of 5-axis Tool Path Motions

Mullineux, G.

Engineering and Physical Sciences Research Council

31/03/14 → 30/03/17

Project: Research council

## Cite this

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