Rodrigues formula for the Cayley transform of groups SO(n) and SE(n)
Keywords:
Lie group, Lie algebra, exponential map, Cayley transform, special orthogonal group SO(n), Euclidean group SE(n), Rodrigues coefficients.Abstract
In Theorem 3.1 we present, in the case when the eigenvalues of the matrix are pairwise distinct, a direct way to determine the Rodrigues coefficients of the Cayley transform for the special orthogonal SO(n) by reducing the Rodrigues problem in this case to the system (3:2). The similar method is discussed for the Euclidean group SE(n).
Mathematics Subject Classification (2010): 22E60, 22E70.
References
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