Minimal matrix centralizers over the field ℤ2
Keywords:
matrix algebra;
centralizer;
minimality;
finite field;
rational canonical form.
Author(s):
David Dolžan, PhD (University of Ljubljana, Faculty of Mathematics and Physics), Damjana Kokol Bukovšek, PhD (University of Ljubljana, Faculty of Economics).
Abstract:
A matrix 
over a field is minimal if for every matrix 
that commutes with 
, the centralizer of 
is a subset of the centralizer of 
. In this paper, we study the minimal matrices over the field with two elements. We characterize the minimal matrices with their minimal polynomial of the form 
, where 
is an irreducible polynomial and 
. We also characterize all minimal matrices with spectrum in 
.
Journal:
Linear and Multilinear Algebra
Indexing:
JCR 106/296
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