Different types of linear transformations on the coordinate plane

rank 0

L carries all points onto the origin.      L(1,0) = (0,0),  L(0,1) = (0,0),      L  very singular

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rank 1

L carries some distinct points onto the same points, but some distinct points onto distinct points
                                                (0,0),   L(1,0),  L(0,1)  collinear but not all the same point

L carries some points onto the origin and some points not onto the origin       L moderately singular


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Rank2

L carries distinct points onto distinct points (1-1)
                                         (0,0),  L(1,0),  L(0,1)  all distinct and not collinear      L non-singular

      inverse of L exist            group of non-singular lintrs   (full linear group)

Special: L preserving length (distance)       (group)   congruence, isometry      special unit square