Isotropy

转自：http://en.wikipedia.org/wiki/Isotropy

Isotropy is uniformity in all orientations; it is derived from the Greekiso (equal) and tropos (direction). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefixan, hence anisotropy.Anisotropy is also used to describe situations where properties vary systematically, dependent on direction.Isotropic radiation has the same intensity regardless of the direction ofmeasurement, and an isotropic field exerts the same action regardless of how the testparticle is oriented.

Mathematics

Within mathematics, isotropy has a few different meanings:

Isotropic manifolds

Some manifolds are isotropic, meaning that thegeometry on the manifold is the same regardless of direction. A similar concept ishomogeneity. A manifold can be homogeneous without being isotropic. But if it is inhomogeneous, it is necessarily anisotropic.

Isotropic quadratic form

A quadratic form q is said to be isotropic if there is a non-zero vector v such thatq(v)=0.

Isotropic coordinates on anIsotropic chart for Lorentzian manifolds.