homogeneous
Part of speech: adj
Morphological type: simple
Topics: algebra
chemistry
geometry
linear-algebra
mathematical-analysis
mathematics
natural-sciences
order-theory
physical-sciences
probability-theory
sciences
set-theory
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).
Inflected forms:
form: homogenous
pos: adj
tags: alternative
Senses:
gloss: Of the same kind; alike, similar.
pos: adj
tags: not-comparable
gloss: Having the same composition throughout; of uniform make-up.
pos: adj
tags: not-comparable
examples: 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.
gloss: In the same state of matter.
pos: adj
tags: not-comparable
gloss: 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.).
pos: adj
tags: not-comparable
gloss: 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.).
pos: adj
tags: not-comparable
examples: The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials
gloss: 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.).
pos: adj
tags: not-comparable
gloss: 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.).
pos: adj
tags: not-comparable
gloss: 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;.
pos: adj
tags: not-comparable
gloss: In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
pos: adj
tags: not-comparable
gloss: In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
pos: adj
tags: not-comparable
gloss: In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
pos: adj
tags: not-comparable
gloss: In abstract algebra and geometry:
pos: adj
tags: not-comparable
gloss: In abstract algebra and geometry:
pos: adj
tags: not-comparable
gloss: In abstract algebra and geometry:
pos: adj
tags: not-comparable
gloss: In abstract algebra and geometry:
pos: adj
tags: not-comparable
gloss: In miscellaneous other senses:
pos: adj
tags: not-comparable
gloss: In miscellaneous other senses:
pos: adj
tags: not-comparable
Synonyms: homogeneous
invariable
of a piece
onefold
samely
uniform
uniformal
unmixed
unvaried
unvarying
Antonyms: heterogeneous
inhomogeneous
Related words: homogeneity
homogenesis
homogenise
homogenize
homogeny
Derived words: bihomogeneous
dishomogeneous
homogeneous broadening
homogeneous catalysis
homogeneous coordinate
homogeneous equilibrium
homogeneous function
homogeneous ideal
homogeneously
homogeneous mixture
homogeneousness
homogeneous number
homogeneous polynomial
homogeneous radiation
homogeneous society
homogeneous space
homogeneous system
homogeneous width
inhomogeneous
nonhomogeneous
prehomogeneous
quasihomogeneous
subhomogeneous
superhomogeneous
time-homogeneous Markovian type
ultrahomogeneous
unhomogeneous
Translations: