Potter, Wielandt, and Drazin on the matrix equation $AB = \omega BA$, with some new answers to old questions

Source file is available as :   Postscript Document

Author(s) : Olga Holtz , Volker Mehrmann , Hans Schneider

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2003

MSC 2000

15A27 Commutativity
15A24 Matrix equations and identities

Abstract :
In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt's for 1951. There he gives a new proof of a theorem due to H.~S.~A.~Potter on the matrix equation $AB = \omega BA$, which is related to the $q$-binomial theorem, and asks some further questions, which we answer. We also describe results by M.~P.~Drazin and others on this equation.

Keywords : Quasi-commutative matrices, q-binomial theorem, normal forms, simultaneous triangularizability