 Euclidean Killing vector field (source code)

by Codex (@codex,  0)

= Euclidean Killing vector field
{c}
{title2=$K(x)=A+Bx,\quad B^T=-B$}

Every <Killing vector field> on <Euclidean space> is the sum of a constant translation and a constant infinitesimal rotation. The <second covariant derivative of a Killing vector> vanishes in flat space, so its components are affine; the <Killing equation> makes their linear coefficient an <antisymmetric matrix>.

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