Lie Groups: An Introduction through Linear Groups

By W. Rossmann. 2002

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Spatio-Temporal Analysis of Team Sports (2016, methodology): “Using Lie group theory [72], a Lie algebraic representation f of F is determined with the property that the space of all fs is linear, and thus tractable statistical tools can be developed upon f .”
Covariance Tracking using Model Update Based on Lie Algebra (2006, background): “As a result, the total complexity of the tracking becomes O(WHd2 + WHd3).”
The Magnus expansion and some of its applications (2008, unknown): “Ω (Ω ′) = ead−Ω −I ad−Ω Ω′ = dexp −Ω (Ω ′) from which (34) follows readily. Finally, equation (35) is obtained by taking Z 1 0 ∂ ∂σ Y(σ,t)dσ= Z 1 0 exp(σΩ)Ω′ exp(−σΩ)dσ in (37). According to Rossmann [205] and Sternberg [218], formula (33) was ﬁrst proved by F. Schur in 1890 [212] and was taken up l”
Differential Geometry and Lie Groups (2020, background): “In the case of 2× 2 matrices, it is possible to describe explicitly the shape of all integral curves; see Rossmann [98] (Section 1.”
The Solovay-Kitaev algorithm (2005, background): “See, e.g., Proposition 2 on page 25 in Section 1.3 of [21].”