Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

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dc.creatorDjokovic, Dragomir Z.
dc.creatorSmith, Benjamin H.
dc.date2007-09-04
dc.date.accessioned2026-07-07T12:52:58Z
dc.date.available2026-07-07T12:52:58Z
dc.descriptionWe construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n by n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.
dc.description26 pages, 2 tables and 2 figures. To appear in Linear Algebra and Its Applications
dc.identifierhttps://arxiv.org/abs/0709.0513
dc.identifierhttp://arxiv.org/abs/0709.0513
dc.identifierLinear Algebra and Its Applications 428 (2008), 890-910
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223470
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.subject15A33; 15A18; 16R30
dc.titleQuaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities
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