Definition:Group Action of GL(2,Q) on Irrational Numbers

Definition
Let $\operatorname{GL} \left({2, \Q}\right)$ be the general linear group on the field of rational numbers.

Let $\R \setminus \Q$ be the set of irrational numbers.

The standard group action of $\operatorname{GL} \left({2, \Q}\right)$ on $\R\setminus \Q$ is the group action:
 * $\operatorname{GL} \left({2, \Q}\right) \times \left({\R \setminus \Q}\right) \to \R \setminus Q$:
 * $\left({\begin {pmatrix} a & b \\

c & d \end {pmatrix}, x}\right) \mapsto \dfrac {a x + b} {c x + d}$

Also see

 * Group Action of GL(2,Q) on Irrational Numbers is Group Action
 * Definition:Group Action of General Linear Group on Projective Line