0. Translations

Definition. A translation is a transformation $T:$   R$^n \rightarrow$   R$^n$ of the form $T($   x$) =$   x$+$   b, where b is a fixed vector.

Example. $T($   x$) =$   x$+ (1,2)$. (See Figure .)

Figure: A translation

book/02dir/trans.eps

Observe that because a translation moves the origin, it is definitely not a homogeneous linear transformation (unless b$=$   0).