# Bojan Kuzma: Matrices with extremal commutants and beyond

Vir: Seminar za algebro in funkcionalno analizo

Abstract:

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