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do a very quick rewrite of the lead section to add some context and wiki-links. someone putting more effort can do much better here |
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where <math>I</math> is the identity matrix, <math>d\theta</math> is vanishingly small, and <math>A \in \mathfrak{so}(n).</math>
For example, if <math>A = L_x,</math> representing an infinitesimal three-dimensional rotation about the {{mvar|x}}-axis, a basis element of <math>\mathfrak{so}(3),</math>
:<math> dL_{x} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & -d\theta \\ 0 & d\theta & 1 \end{bmatrix}. </math>
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