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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Lie Groups II: Differential-Geometric Properties
verfasst von : Gregory S. Chirikjian
Erschienen in: Stochastic Models, Information Theory, and Lie Groups, Volume 2
Verlag: Birkhäuser Boston
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This chapter discusses how a natural extension of the concept of directional derivatives in R
n
can be defined for functions on Lie groups. This “Lie derivative” is closely related to the differential geometric properties of the group. Functions on a Lie group can be expanded in a Taylor series using Lie derivatives. Explicit expressions for these Lie derivatives in a particular parametrization can be easily obtained for Lie groups using the appropriate concept of a Jacobian matrix as defined in the previous chapter.