Potter, Wielandt, and Drazin on the matrix equation $AB=\omega BA$, with some new answers to old questions
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In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt's for 1951.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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2005
 arXiv:
 arXiv:math/0512607
 Bibcode:
 2005math.....12607H
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  History and Overview;
 15A27;
 15A24;
 01A70
 EPrint:
 18 pages, 1 picture, 1 facsimile. A shorter version of this paper is published in Amer. Math. Monthly 111 (2004), no. 8, 655667