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note, we display a page of an unpublished mathematical diary of Helmut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