Editing Isotropy (section)

==Mathematics==
Within [[mathematics]], ''isotropy'' has a few different meanings:
; [[Isotropic manifold]]s: A [[manifold]] is isotropic if the [[geometry]] on the manifold is the same regardless of direction. A similar concept is [[homogeneous space|homogeneity]]. 
; [[Isotropic quadratic form]]: A [[quadratic form]] ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that {{nowrap|1=''q''(''v'') = 0}}; such a ''v'' is an [[isotropic vector]] or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an [[isotropic line]].
; [[Isotropic coordinates]]: Isotropic coordinates are coordinates on an isotropic chart for [[Lorentzian manifolds]].
; [[Isotropy group]]:An isotropy group is the group of [[isomorphism]]s from any [[object (category theory)|object]] to itself in a [[groupoid]].{{dubious|date=December 2018}}<ref>A [[groupoid]] <math>\mathcal G</math> is a [[category (mathematics)|category]] where all [[morphism]]s are [[isomorphism]]s, i.e., invertible. If <math>G \in \mathcal G</math> is any object, then <math>\mathcal G(G,G)</math> denotes its [[isotropy group]]: the group of isomorphisms from <math>G</math> to <math>G</math>.</ref> An [[isotropy representation]] is a representation of an isotropy group.
; [[Isotropic position]]: A [[probability distribution]] over a [[vector space]] is in isotropic position if its [[covariance matrix]] is the [[identity matrix|identity]]. 
; [[Isotropic vector field]]: The [[vector field]] generated by a point source is said to be ''isotropic'' if, for any spherical neighborhood centered at the point source, the magnitude of the vector determined by any point on the sphere is invariant under a change in direction. For an example, starlight appears to be isotropic.