homogeneous
/ˌhoʊ.moʊˈd͡ʒi.ni.əs/
Frequency: 3.22 in modern English
Meaning
adj
Having the same composition throughout; of uniform make-up.
adj
In the same state of matter.
adj
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.).
adj
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.).
adj
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.).
adj
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.).
adj
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."
- "The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials"
Etymology
Origin
Word Breakdown
- Root: homogeneus, ὁμογενής
Regional Pronunciation
- American English: /ˌhoʊ.moʊˈd͡ʒi.ni.əs/
- British English: /ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/