adj
Meaning 1
Of the same kind; alike, similar.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Standard Lemma guide
homogeneous
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
Sound
Pronunciation
Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.
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UK: /ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/
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UK: /ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/
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Gloucestershire Recorded audio is listed in the source snapshot.
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US: /ˌhoʊ.moʊˈd͡ʒi.ni.əs/
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US: /ˌhoʊ.mə-/
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US: /-ˈd͡ʒɛ-/
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US: /-njəs/
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US: /həˈmɑ.d͡ʒə.nəs/
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General-American: Recorded audio is listed in the source snapshot.
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General-American: Recorded audio is listed in the source snapshot.
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General-American: Recorded audio is listed in the source snapshot.
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CMU ARPABET: HH OW2 M AH0 JH IY1 N IY0 AH0 S Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.
adj
Meaning 2
Having the same composition throughout; of uniform make-up.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 3
In the same state of matter.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: chemistry, natural-sciences, physical-sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 4
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.).
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 5
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: algebra, mathematics, sciences
Examples
- The polynomial x2+5xy+y2 is homogeneous of degree 2, because x2, xy, and y2 are all degree 2 monomials
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 6
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: by specialization
Topics: linear-algebra, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 7
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(
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: generalizing the case of polynomial functions
Topics: mathematical-analysis, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 8
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;.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 9
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 10
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 11
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 12
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)
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: ring theory
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 13
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 14
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).
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: geometry, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 15
In abstract algebra and geometry:
Of or relating to homogeneous coordinates.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: geometry, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 16
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: Fourier analysis
Topics: mathematics, probability-theory, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 17
In miscellaneous other senses:
Holding between a set and itself; being an endorelation.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: mathematics, order-theory, sciences, set-theory
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adjective
Meaning 18
all of the same or similar kind or nature
Definition source: Princeton WordNet 3.0
Examples
- a close-knit homogeneous group
Meaning relationships
Synonyms: homogenous
Antonyms: heterogeneous
History
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).
Across languages
Translations
67 source translations are retained for this English entry.
- Afrikaans: homogeen — of the same kind; alike, similar
- Albanian: homogjen — of the same kind; alike, similar
- Armenian: միատարր (miatarr) — of the same kind; alike, similar
- Armenian: համասեռ (hamaseṙ) — of the same kind; alike, similar
- Bulgarian: еднороден (ednoroden) — of the same kind; alike, similar
- Catalan: homogeni — of the same kind; alike, similar
- Chinese Mandarin: 同質 /同质 (tóngzhí, tóngzhì) — of the same kind; alike, similar
- Czech: stejnorodý — of the same kind; alike, similar
- Czech: homogenní — of the same kind; alike, similar
- Dutch: homogeen — of the same kind; alike, similar
- Finnish: samanlainen — of the same kind; alike, similar
- Finnish: homogeeninen — of the same kind; alike, similar
- French: homogène — of the same kind; alike, similar
- Galician: homoxéneo — of the same kind; alike, similar
- German: homogen — of the same kind; alike, similar
- German: gleichartig — of the same kind; alike, similar
- Greek: ομογενής (omogenís) — of the same kind; alike, similar
- Greek: ομοιογενής (omoiogenís) — of the same kind; alike, similar
- Hungarian: homogén — of the same kind; alike, similar
- Icelandic: einsleitur — of the same kind; alike, similar
- Icelandic: einleitur — of the same kind; alike, similar
- Icelandic: eingerður — of the same kind; alike, similar
- Icelandic: samkynja — of the same kind; alike, similar
- Icelandic: samleitur — of the same kind; alike, similar
- Indonesian: homogen — of the same kind; alike, similar
- Irish: aonchineálach — of the same kind; alike, similar
- Italian: omogeneo — of the same kind; alike, similar
- Japanese: 均質 (kinshitsu) — of the same kind; alike, similar
- Japanese: 同質 (dōshitsu) — of the same kind; alike, similar
- Kazakh: гомогендік (gomogendık) — of the same kind; alike, similar
- Kazakh: біртекті (bırtektı) — of the same kind; alike, similar
- Macedonian: еднообразен (ednoobrazen) — of the same kind; alike, similar
- Macedonian: еднороден (ednoroden) — of the same kind; alike, similar
- Macedonian: хомоген (homogen) — of the same kind; alike, similar
- Manx: cocheintagh — of the same kind; alike, similar
- Norwegian Bokmål: homogen — of the same kind; alike, similar
- Norwegian Nynorsk: homogen — of the same kind; alike, similar
- Polish: jednorodny — of the same kind; alike, similar
- Polish: jednolity — of the same kind; alike, similar
- Portuguese: homogêneo — of the same kind; alike, similar
- Portuguese: homogéneo — of the same kind; alike, similar
- Romanian: omogen — of the same kind; alike, similar
- Russian: одноро́дный (odnoródnyj) — of the same kind; alike, similar
- Russian: гомоге́нный (gomogénnyj) — of the same kind; alike, similar
- Russian: единообра́зный (jedinoobráznyj) — of the same kind; alike, similar
- Spanish: homogéneo — of the same kind; alike, similar
- Swedish: homogen — of the same kind; alike, similar
- Swedish: enhetlig — of the same kind; alike, similar
- Tagalog: tulad-uriin — of the same kind; alike, similar
- Telugu: సజాతి (sajāti) — of the same kind; alike, similar
- Armenian: համասեռ (hamaseṙ) — having the same composition throughout
- Bulgarian: еднороден (ednoroden) — having the same composition throughout
- Bulgarian: хомогенен (homogenen) — having the same composition throughout
- Catalan: homogeni — having the same composition throughout
- Finnish: tasa-aineinen — having the same composition throughout
- Finnish: homogeeninen — having the same composition throughout
- French: homogène — having the same composition throughout
- Italian: omogeneo — having the same composition throughout
- Macedonian: еднороден (ednoroden) — having the same composition throughout
- Macedonian: еднообразен (ednoobrazen) — having the same composition throughout
- Macedonian: хомоген (homogen) — having the same composition throughout
- Māori: kanorite — having the same composition throughout
- Persian: هملوناء — having the same composition throughout
- Portuguese: homogêneo — having the same composition throughout
- Spanish: homogéneo — having the same composition throughout
- Swedish: homogen — having the same composition throughout
- Tagalog: tulad-uriin — having the same composition throughout