Let A be a set, and T:AA a transformation of that set. We say that xA is an invariant of T whenever x is fixed by T:


We say that a subset BA is invariant with respect to T whenever


If this is so, the restrictionPlanetmathPlanetmathPlanetmath of T is a well-defined transformation of the invariant subset:


The definition generalizes readily to a family of transformations with common domain


In this case we say that a subset is invariant, if it is invariant with respect to all elements of the family.

Title invariant
Canonical name Invariant
Date of creation 2013-03-22 12:26:09
Last modified on 2013-03-22 12:26:09
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 8
Author rmilson (146)
Entry type Definition
Classification msc 03E20
Related topic Transformation
Related topic InvariantSubspace
Related topic Fixed