To transform
something is to change it in some way. A transformation is what
brings about the change. It may transform a set of numbers or a
set of points. The transformation n ^{__}> 7 - n, for example
will transform a magic triangle containing the numbers
1 to 6 into a different magic triangle with the same numbers.

There are many
kinds of geometric transformations, ranging from translations which
move on object to a new position without changing its shape, size
or direction, to topological transformations which can considerably
distort a shape. In between these there are the rotations, reflections,
enlargements, stretches and shears. Geometrical transformations
can be represented by matrices.