PAIRS OF MATRICES, ONE OF WHICH COMMUTES WITH THEIR COMMUTATOR

@article{Bourgeois2011PAIRSOM,
  title={PAIRS OF MATRICES, ONE OF WHICH COMMUTES WITH THEIR COMMUTATOR},
  author={G. Bourgeois},
  journal={Electronic Journal of Linear Algebra},
  year={2011},
  volume={22},
  pages={38}
}
  • G. Bourgeois
  • Published 2011
  • Mathematics
  • Electronic Journal of Linear Algebra
Let A, B be n × n complex matrices such that C = AB BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n � 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… Expand
2 Citations
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