The tensor rank problem over the quaternions

dc.contributor.authorLiang, YG
dc.contributor.examiningcommitteeKucera, Tommy (Mathematics)en_US
dc.contributor.examiningcommitteeKrepski, Derek (Mathematics)en_US
dc.contributor.examiningcommitteeWang, Dingkang (Chinese Academy of Sciences)en_US
dc.contributor.supervisorZhang, Yang
dc.date.accessioned2023-01-16T21:34:24Z
dc.date.available2023-01-16T21:34:24Z
dc.date.copyright2022-12-30
dc.date.issued2022-12-30
dc.date.submitted2022-12-30T19:36:52Zen_US
dc.degree.disciplineMathematicsen_US
dc.degree.levelDoctor of Philosophy (Ph.D.)en_US
dc.description.abstractIn 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.noteFebruary 2023en_US
dc.identifier.urihttp://hdl.handle.net/1993/37129
dc.language.isoengen_US
dc.rightsopen accessen_US
dc.subjecttensor rank, tensor decomposition, quaternionen_US
dc.titleThe tensor rank problem over the quaternionsen_US
dc.typedoctoral thesisen_US
local.subject.manitobanoen_US
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