Editing Vector field (section)

===Central field in euclidean spaces===
A {{math|''C''<sup>∞</sup>}}-vector field over {{math|'''R'''<sup>''n''</sup> \ {0}<nowiki/>}} is called a '''central field''' if
<math display="block">V(T(p)) = T(V(p)) \qquad (T \in \mathrm{O}(n, \R))</math>
where {{math|O(''n'', '''R''')}} is the [[orthogonal group]]. We say central fields are [[invariant (mathematics)|invariant]] under [[Orthogonal matrix|orthogonal transformations]] around 0.

The point 0 is called the '''center''' of the field.

Since orthogonal transformations are actually rotations and reflections, the invariance conditions mean that vectors of a central field are always directed towards, or away from, 0; this is an alternate (and simpler) definition. A central field is always a gradient field, since defining it on one semiaxis and integrating gives an antigradient.