Infinitesimal transformation

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In mathematics, an infinitesimal transformation is a limiting form of small transformation. For example one may talk about an infinitesimal rotation of a rigid body, in three-dimensional space. This is conventionally represented by a 3×3 skew-symmetric matrix A. It is not the matrix of an actual rotation in space; but for small real values of a parameter ε the transformation

${\displaystyle T=I+\varepsilon A}$

is a small rotation, up to quantities of order ε².