Geodesic
Pairs of matrices, one of which commutes with their commutator
The electronic journal of linear algebra, Tome 22 (2011), pp. 593-597.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let A, B be n $\times n$ complex matrices such that C = AB - BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n $\geq 3$, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of the Alp'in-Koreshkov's algorithm that checks whether two matrices are simultaneously triangularizable. Practically, one cannot test a pair of numerical matrices of dimension greater than five.
Classification : 15A27, 15A22
Keywords: nilpotent matrix, property L, commutator, quasi-commute 
@article{ELA_2011__22__a39,
     author = {Bourgeois, Gerald},
     title = {Pairs of matrices, one of which commutes with their commutator},
     journal = {The electronic journal of linear algebra},
     pages = {593--597},
     publisher = {mathdoc},
     volume = {22},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2011__22__a39/}
}
TY  - JOUR
AU  - Bourgeois, Gerald
TI  - Pairs of matrices, one of which commutes with their commutator
JO  - The electronic journal of linear algebra
PY  - 2011
SP  - 593
EP  - 597
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2011__22__a39/
LA  - en
ID  - ELA_2011__22__a39
ER  - 
%0 Journal Article
%A Bourgeois, Gerald
%T Pairs of matrices, one of which commutes with their commutator
%J The electronic journal of linear algebra
%D 2011
%P 593-597
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2011__22__a39/
%G en
%F ELA_2011__22__a39
Bourgeois, Gerald. Pairs of matrices, one of which commutes with their commutator. The electronic journal of linear algebra, Tome 22 (2011), pp. 593-597. http://geodesic.mathdoc.fr/item/ELA_2011__22__a39/