COMMUTATORS OF SKEW-SYMMETRIC MATRICES-Reference-Cited by-同舟云学术

COMMUTATORS OF SKEW-SYMMETRIC MATRICES

Published:2005-03 Issue:03 Volume:15 Page:793-801
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

BLOCH ANTHONY M.¹,ISERLES ARIEH²

Affiliation:

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

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

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 [Formula: see text], X, Y ∈ 𝔰𝔬(n), 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127405012417

Reference12 articles.

1. Differential equations and matrix inequalities on isospectral families

2. Lectures on Lie Groups and Lie Algebras

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