Dictionary

homogeneous en · ADJ

Pronunciation

(General-American) audio
(General-American) audio
/ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/ (UK)
/ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/ (UK)
/-ˈd͡ʒɛ-/ (US)
/ˌhoʊ.mə-/ (US)
audio Gloucestershire
/-njəs/ (US)
/həˈmɑ.d͡ʒə.nəs/ (US)
(General-American) audio
/ˌhoʊ.moʊˈd͡ʒi.ni.əs/ (US)

Etymology

From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

Meanings

(not-comparable) Of the same kind; alike, similar.
(not-comparable) Having the same composition throughout; of uniform make-up.
- All pseudolatex formulations were homogeneous and smooth in texture and elegant in appearance. 2013 October 14, Jirapornchai Suksaeree, Laksana Charoenchai, Chaowalit Monton, Tun Chusut, Apirak Sakunpak, Wiwat Pichayakorn and Prapaporn Boonme, “Preparation of a Pseudolatex-Membrane for Ketoprofen Transdermal Drug Delivery Systems”, in Industrial & Engineering Chemistry Research, volume 52, number 45, →DOI:
- Their citizens were not of homogeneous origin, but were from all parts of Greece. 1946, Bertrand Russell, History of Western Philosophy, I.25:
(not-comparable) In the same state of matter.
(not-comparable) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
(not-comparable, of a polynomial) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.). ▸ Of polynomials, functions, equations, systems of equations, or linear maps: ▸ Such that all its nonzero terms have the same degree.
- The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials
(not-comparable, of a system of linear equations, qualifier:by specialization) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.). ▸ Of polynomials, functions, equations, systems of equations, or linear maps: ▸ Such that all the constant terms are zero.
(not-comparable, of a function f, qualifier:generalizing the case of polynomial functions) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.). ▸ Of polynomials, functions, equations, systems of equations, or linear maps: ▸ Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
(not-comparable) The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
(not-comparable, of a first-order differential equation) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity): ▸ Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
(not-comparable, of a linear differential equation) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity): ▸ Having its degree-zero term equal to zero; admitting the trivial solution.
(not-comparable, of a general differential equation) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity): ▸ Homogeneous as a function of the dependent variable and its derivatives.
(not-comparable, of an element of a graded ring, qualifier:ring theory) In abstract algebra and geometry: ▸ Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
(not-comparable, of a linear map f between vector spaces graded by a commutative monoid I) In abstract algebra and geometry: ▸ Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
(not-comparable, of a space equipped with a group action) In abstract algebra and geometry: ▸ Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
(not-comparable) In abstract algebra and geometry: ▸ Of or relating to homogeneous coordinates.
(not-comparable, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0), qualifier:Fourier analysis) In miscellaneous other senses: ▸ Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
(not-comparable, of a relation) In miscellaneous other senses: ▸ Holding between a set and itself; being an endorelation.

Forms

Spelling	Features	Labels	Source
homogenous		alternative	lexicographic

Translations (67)

ca homogeni (having the same composition throughout) · bg еднороден (having the same composition throughout) · es homogéneo (having the same composition throughout) · mk еднообразен (having the same composition throughout) · de gleichartig (of the same kind; alike, similar) · tl tulad-uriin (of the same kind; alike, similar) · mk еднороден (of the same kind; alike, similar) · mk еднообразен (of the same kind; alike, similar) · sv enhetlig (of the same kind; alike, similar) · ja 同質 (of the same kind; alike, similar) · nb homogen (of the same kind; alike, similar) · fi homogeeninen (having the same composition throughout) · af homogeen (of the same kind; alike, similar) · fi homogeeninen (of the same kind; alike, similar) · hy միատարր (of the same kind; alike, similar) · mk хомоген (of the same kind; alike, similar) · es homogéneo (of the same kind; alike, similar) · bg еднороден (of the same kind; alike, similar) · is samleitur (of the same kind; alike, similar) · sq homogjen (of the same kind; alike, similar) · ru одноро́дный (of the same kind; alike, similar) · fi samanlainen (of the same kind; alike, similar) · ro omogen (of the same kind; alike, similar) · bg хомогенен (having the same composition throughout) · is einleitur (of the same kind; alike, similar) · ru единообра́зный (of the same kind; alike, similar) · it omogeneo (having the same composition throughout) · mk хомоген (having the same composition throughout) · kk біртекті (of the same kind; alike, similar) · pl jednorodny (of the same kind; alike, similar) · it omogeneo (of the same kind; alike, similar) · id homogen (of the same kind; alike, similar) · el ομοιογενής (of the same kind; alike, similar) · gv cocheintagh (of the same kind; alike, similar) · ja 均質 (of the same kind; alike, similar) · fr homogène (of the same kind; alike, similar) · ca homogeni (of the same kind; alike, similar) · pt homogéneo (of the same kind; alike, similar) · nl homogeen (of the same kind; alike, similar) · ru гомоге́нный (of the same kind; alike, similar) · is eingerður (of the same kind; alike, similar) · fr homogène (having the same composition throughout) · el ομογενής (of the same kind; alike, similar) · te సజాతి (of the same kind; alike, similar) · hy համասեռ (having the same composition throughout) · cs stejnorodý (of the same kind; alike, similar) · de homogen (of the same kind; alike, similar) · hy համասեռ (of the same kind; alike, similar) · fa هملوناء (having the same composition throughout) · mk еднороден (having the same composition throughout) · cs homogenní (of the same kind; alike, similar) · pt homogêneo (having the same composition throughout) · sv homogen (of the same kind; alike, similar) · is einsleitur (of the same kind; alike, similar) · is samkynja (of the same kind; alike, similar) · kk гомогендік (of the same kind; alike, similar) · gl homoxéneo (of the same kind; alike, similar) · ga aonchineálach (of the same kind; alike, similar) · cmn 同質 /同质 (of the same kind; alike, similar) · mi kanorite (having the same composition throughout) · hu homogén (of the same kind; alike, similar) · pt homogêneo (of the same kind; alike, similar) · pl jednolity (of the same kind; alike, similar) · nn homogen (of the same kind; alike, similar) · tl tulad-uriin (having the same composition throughout) · fi tasa-aineinen (having the same composition throughout) · sv homogen (having the same composition throughout)

homogeneous en · ADJ

Pronunciation

Etymology

Meanings

Forms

Antonyms

Deriveds

Hyponyms

Relateds

Synonyms

Translations (67)