fix (transformation action)

Let A be a set, and T:AA a transformationPlanetmathPlanetmath of that set. We say that xA is fixed by T, or that T fixes x, whenever


The subset of fixed elements is called the fixed set of T, and is frequently denoted as AT.

We say that a subset BA is fixed by T whenever all elements of B are fixed by T, i.e.


If this is so, T restricts to the identity transformation on B.

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


In this case we say that a subset BA is fixed, if it is fixed by all the elements of the family, i.e. whenever

Title fix (transformation action)
Canonical name FixtransformationAction
Date of creation 2013-03-22 12:26:12
Last modified on 2013-03-22 12:26:12
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 15
Author rmilson (146)
Entry type Definition
Classification msc 03E20
Synonym fix
Synonym fixed
Synonym fixes
Related topic Invariant
Related topic Transformation
Related topic Fix2
Defines fixed set