Editing Rotational invariance (section)

=== Operators ===

For a [[function (mathematics)|function]]
: <math>f : X \rightarrow X ,</math>
which maps elements from a [[subset]] ''X'' of the [[real line]] <math>\mathbb{R}</math> to itself, '''rotational invariance''' may also mean that the function [[commutative operation|commute]]s with rotations of elements in ''X''. This also applies for an [[Operator (mathematics)|operator]] that acts on such functions. An example is the two-dimensional [[Laplace operator]] 
: <math>\nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} ,</math>
which acts on a function ''f'' to obtain another function ∇<sup>2</sup>''f''. This operator is invariant under rotations.

If ''g'' is the function ''g''(''p'') = ''f''(''R''(''p'')), where ''R'' is any rotation, then (∇<sup>2</sup>''g'')(''p'') = (∇<sup>2</sup>''f'' )(''R''(''p'')); that is, rotating a function merely rotates its Laplacian.  <!-- Should add the (classical) physics sense, and Computer Vision sense too -->