Potter, Wielandt, and Drazin on the matrix equation $AB=\omega BA$, with some new answers to old questions
In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt's for 1951.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.
arXiv Mathematics e-prints
- Pub Date:
- December 2005
- Mathematics - Rings and Algebras;
- Mathematics - History and Overview;
- 18 pages, 1 picture, 1 facsimile. A shorter version of this paper is published in Amer. Math. Monthly 111 (2004), no. 8, 655--667