Homogeneous

/ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/ · adjective

Meaning

Of the same kind; alike, similar..

Definitions by Sense

1. Of the same kind; alike, similar.
2. Having the same composition throughout; of uniform make-up.
3. (chemistry) In the same state of matter.
4. (mathematics) 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.).
5. 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;.
6. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
7. In abstract algebra and geometry:
8. In miscellaneous other senses:

Example Sentences

Their citizens were not of homogeneous origin, but were from all parts of Greece.

All pseudolatex formulations were homogeneous and smooth in texture and elegant in appearance.

Synonyms for homogeneous

Antonyms for homogeneous

Related Words

Word Forms

• homogenous

Usage Notes

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