Infinitesimal rotation matrix

An infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix R T = R − 1 {\displaystyle R^{\mathsf {T}}=R^{-1}} representing an element of S O ( n ) {\displaystyle \mathrm {SO} (n)} (the special orthogonal group), the differential of a rotation is a skew-symmetric matrix A T = − A {\displaystyle A^{\mathsf {T}}=-A} in the tangent space s o ( n ) {\displaystyle {\mathfrak {so}}(n)} (the special orthogonal Lie algebra), which is not itself a rotation matrix.

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