Homothety and Uniform Scaling
If the homothetic center S happens to coincide with the origin O of the vector space (S ≡ O), then every homothety with scale factor λ is equivalent to a uniform scaling by the same factor, which sends
As a consequence, in the specific case in which S ≡ O, the homothety becomes a linear transformation, which preserves not only the collinearity of points (straight lines are mapped to straight lines), but also vector addition and scalar multiplication.
Read more about this topic: Homothetic Transformation
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