Pairs of mutually annihilating operators

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dc.creatorBondarenko, Vitalij M.
dc.creatorGerasimova, Tatiana G.
dc.creatorSergeichuk, Vladimir V.
dc.date2008-12-11
dc.date.accessioned2026-07-07T12:12:01Z
dc.date.available2026-07-07T12:12:01Z
dc.descriptionPairs (A,B) of mutually annihilating operators AB=BA=0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1-58] by method of linear relations. The classification of (A,B) over any field was derived by Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636-654] from the classification of finitely generated modules over a dyad of two local Dedekind rings. We give canonical matrices of (A,B) over any field in an explicit form and our proof is constructive: the matrices of (A,B) are sequentially reduced to their canonical form by similarity transformations (A,B)--> S^{-1}AS, S^{-1}BS).
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0812.2155
dc.identifierhttp://arxiv.org/abs/0812.2155
dc.identifierLinear Algebra Appl. 430 (2009) 86-105
dc.identifierdoi:10.1016/j.laa.2008.06.038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210409
dc.subjectRepresentation Theory
dc.subjectFunctional Analysis
dc.subject15A21
dc.titlePairs of mutually annihilating operators
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