A matrix-based proof of the quaternion representation theorem for four-dimensional rotations
| dc.creator | Mebius, Johan Ernest | |
| dc.date | 2005-01-16 | |
| dc.date.accessioned | 2026-07-07T05:16:07Z | |
| dc.date.available | 2026-07-07T05:16:07Z | |
| dc.description | To each 4x4 matrix of reals another 4x4 matrix is constructed, the so-called associate matrix. This associate matrix is shown to have rank 1 and norm 1 (considered as a 16D vector) if and only if the original matrix is a 4D rotation matrix. This rank-1 matrix is the dyadic product of a pair of 4D unit vectors, which are determined as a pair up to their signs. The leftmost factor (the column vector) consists of the components of the left quaternion and represents the left-isoclinic part of the 4D rotation. The rightmost factor (the row vector) likewise represents the right quaternion and the right-isoclinic part of the 4D rotation. Finally the intrinsic geometrical meaning of this matrix-based proof is established by means of the usual similarity transformations. | |
| dc.description | 5 references; about 3000 words | |
| dc.identifier | https://arxiv.org/abs/math/0501249 | |
| dc.identifier | http://arxiv.org/abs/math/0501249 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73868 | |
| dc.subject | General Mathematics | |
| dc.subject | 20G20 (Primary), 51N20 (Secondary) | |
| dc.title | A matrix-based proof of the quaternion representation theorem for four-dimensional rotations | |
| dc.type | text |