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COMMUTATORS OF SKEW-SYMMETRIC MATRICES

Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

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Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England

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https://doi.org/10.1142/9789812774569_0005Cited by:0 (Source: Crossref)

Abstract:

In this paper we develop a theory for analysing the “radius” of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra so(n) of skew symmetric matrices where we prove , for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control.