Bojan Kuzma: Matrices with extremal commutants and beyond

Datum objave: 12. 3. 2018
Seminar za algebro in funkcionalno analizo
Četrtek, 15. 3. 2018, ob 12:30 v predavalnici 2.04, FMF, Jadranska 21, Ljubljana


Matrices whose commutant is either maximal or minimal with respect to set-inclusion were classified in 2005 by Dolinar and \v Semrl in their pursuit towards classification of bijections which preserve zeros of Lie product. The classification which they obtained is valid only for complex matrices. Recently, we extended their classification in several directions:
(a) For matrices over an arbitrary field. Besides the  classes that were obtained in the complex case  some new possibilities are here possible.
(b) We also investigated the problems of these kind within certain subclasses of (complex) matrices, in particular within doubly stochastic matrices.
(c) Instead of commutativity one may further consider the commutativity up to a factor \xi, defined by AB = \xi BA and classify matrices which are extremal with respect to this relation.

The aim of the talk is to present the obtained results. This is a joint work with many collaborators.


Vljudno vabljeni!                             

Roman Drnovšek in Primož Moravec