homothety

Meanings

Plural: homotheties

Noun

An isotropic scaling transformation of an affine space with a single fixed point.
A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case).

Origin / Etymology

From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).

Synonyms

homogeneous dilation, homothecy, homothetic transformation

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