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

Details Potter, Wielandt, and Drazin on the matrix equation $AB=ωBA$, with some new answers to old questions Potter, Wielandt, and Drazin on the matrix equation $AB=ωBA$, with some new answers to old questions

2005-12-27

arxiv.org/abs/math/0512607v1

Mathematics

Rings and Algebras

18 pages, 1 picture, 1 facsimile. A shorter version of this paper is published in Amer. Math. Monthly 111 (2004), no. 8, 655--

Scientific paper

In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt's for 1951.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.

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