Homogeneous

Quick meaning: Homogeneous is an adjective meaning Of the same kind; alike, similar.

Meaning

Of the same kind; alike, similar.

More Meanings

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

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.

Word Forms

• homogenous

Synonyms for homogeneous

Depending on context, synonyms include invariable, onefold, samely, uniform, uniformal, unmixed.

Antonyms for homogeneous

Common opposites include heterogeneous, inhomogeneous.

Related Words

Related dictionary entries include solid, homogenized, uniform, consistent, homogeneity, homogenous.

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