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Pairs of mutually annihilating operators
Authors:Vitalij M Bondarenko  Vladimir V Sergeichuk
Institution:a Institute of Mathematics, Tereshchenkivska 3, Kiev, Ukraine
b Mech.-Math. Faculty, Kiev National University, Vladimirskaja 64, Kiev, Ukraine
Abstract:Pairs (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-1AS,S-1BS).
Keywords:15A21
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