Infinitesimal rotation matrix: Difference between revisions

Revision as of 16:57, 17 May 2023

Revision as of 17:26, 17 May 2023

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An '''infinitesimal rotation matrix''' or '''differential rotation matrix''' is a [[matrix (mathematics)|matrix]] representing an [[infinitesimal|infinitely]] slightsmall [[rotation]].

While a [[rotation matrix]] is an [[orthogonal matrix]] <math>R^\mathsf{T} = R^{-1}</math> representing an element of <math>SO(n)</math> (the [[special orthogonal group]]), the [[differential (mathematics)|differential]] of a rotation is a [[skew-symmetric matrix]] <math>A^\mathsf{T} = -A</math> in the [[tangent space]] <math>\mathfrak{so}(n)</math> (the [[special orthogonal Lie algebra]]), which is not itself a rotation matrix.