homothety.
An isotropic scaling transformation of an affine space with a single fixed point.
Meaning & usage
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).
Where this word comes from
From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.