### Abstract

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 |

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### Cite this

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

*230*(18), 3267-3273. https://doi.org/10.1177/0954406215609943

**Characterizing isoclinic matrices and the Cayley factorization.** / Hunt, Matthew; Mullineux, Glen; Cripps, Robert J.; Cross, Ben.

Research output: Contribution to journal › Article

*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*, vol. 230, no. 18, pp. 3267-3273. https://doi.org/10.1177/0954406215609943

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TY - JOUR

T1 - Characterizing isoclinic matrices and the Cayley factorization

AU - Hunt, Matthew

AU - Mullineux, Glen

AU - Cripps, Robert J.

AU - Cross, Ben

PY - 2016/11

Y1 - 2016/11

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1177/0954406215609943

U2 - 10.1177/0954406215609943

DO - 10.1177/0954406215609943

M3 - Article

VL - 230

SP - 3267

EP - 3273

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

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

SN - 0954-4062

IS - 18

ER -