Commutators of Skew-Symmetric Matrices

@article{Bloch2005CommutatorsOS,
  title={Commutators of Skew-Symmetric Matrices},
  author={Anthony M. Bloch and Arieh Iserles},
  journal={I. J. Bifurcation and Chaos},
  year={2005},
  volume={15},
  pages={793-801}
}
In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g and a norm ‖ · ‖ : g → R+, what is the size of ‖[X,Y ‖ in comparison with ‖X‖ · ‖Y ‖? On the face of… CONTINUE READING

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