Mathematics – Representation Theory
Scientific paper
2008-12-11
Linear Algebra Appl. 430 (2009) 86-105
Mathematics
Representation Theory
28 pages
Scientific paper
10.1016/j.laa.2008.06.038
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^{-1}AS, S^{-1}BS).
Bondarenko Vitalij M.
Gerasimova Tatiana G.
Sergeichuk Vladimir V.
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