geometric transformation translations rotations reflections rigid motions isometries projections homographies Möbius transformations projective space map linear maps lines
Most geometric transformation, such as translations, rotations, reflections, rigid motions, isometries, and projections transform lines into lines. It follows that they can be defined, specified and studied in terms of linear maps. This is also the case of homographies and Möbius transformations, when considered as transformations of a projective space.
