The tensor rank problem over the quaternions
| dc.contributor.author | Liang, YG | |
| dc.contributor.examiningcommittee | Kucera, Tommy (Mathematics) | en_US |
| dc.contributor.examiningcommittee | Krepski, Derek (Mathematics) | en_US |
| dc.contributor.examiningcommittee | Wang, Dingkang (Chinese Academy of Sciences) | en_US |
| dc.contributor.supervisor | Zhang, Yang | |
| dc.date.accessioned | 2023-01-16T21:34:24Z | |
| dc.date.available | 2023-01-16T21:34:24Z | |
| dc.date.copyright | 2022-12-30 | |
| dc.date.issued | 2022-12-30 | |
| dc.date.submitted | 2022-12-30T19:36:52Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | en_US |
| dc.description.abstract | In this thesis, we give the maximal rank (the best possible upper bound) of quaternionic tensors in the some small cases. Decomposition of a quaternionic tensor into simple tensors in the some of these cases are discussed. We also give an example of a complex tensor that has different ranks over the complex field and the real quaternion algebra. Moreover, we give the maximal rank and canonical forms of arbitrary quaternionic 3-tensors with 2 frontal slices. We also discuss some upper bounds for general quaternion tensors by using a block tensor approach. | en_US |
| dc.description.note | February 2023 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/37129 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | tensor rank, tensor decomposition, quaternion | en_US |
| dc.title | The tensor rank problem over the quaternions | en_US |
| dc.type | doctoral thesis | en_US |
| local.subject.manitoba | no | en_US |