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On the uniform finite generation of SO(n,R)

Authors
Journal
Systems & Control Letters
0167-6911
Publisher
Elsevier
Publication Date
Volume
2
Issue
6
Identifiers
DOI: 10.1016/0167-6911(83)90042-7
Keywords
  • Lie Groups
  • Symmetric Spaces
  • Vector Fields
  • Uniform Generation
  • Special Orthogonal Group
  • Permutation Matrices

Abstract

Abstract A Lie group G, generated by two one-parameter subgroups is said to be uniformly finitely generated by them if there exists a positive integer N such that every element of G can be expressed as a product of at most N elements chosen alternately from the two one-parameter subgroups. In this paper we construct pairs of generators of so( n) whose one-parameter subgroups uniformly finitely generate SO( n) and as a consequence, we put an upper bound on the number of switches required to join any two points on a manifold M trajectories of two particular vector fields on M.

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