homogeneous

adj

1. (not-comparable)Of the same kind; alike, similar.
2. (not-comparable)Having the same composition throughout; of uniform make-up.

   “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.”

3. (not-comparable)In the same state of matter.
4. (not-comparable)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. (not-comparable)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.).

   “The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials”

6. (not-comparable)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. (not-comparable)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.).
8. (not-comparable)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;.
9. (not-comparable)In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
10. (not-comparable)In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
11. (not-comparable)In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
12. (not-comparable)In abstract algebra and geometry:
13. (not-comparable)In abstract algebra and geometry:
14. (not-comparable)In abstract algebra and geometry:
15. (not-comparable)In abstract algebra and geometry:
16. (not-comparable)In miscellaneous other senses:
17. (not-comparable)In miscellaneous other senses: