homogeneous

Etymology

Definitions

1. 1

   Of the same kind

   Of the same kind; alike, similar.

2. 2

   Having the same composition throughout

   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. 3

   In the same state of matter.

4. ›+ 5 more definitionsshow fewer

   1. 4

      In any of several technical senses uniform

      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.).

   2. 5

      The function f(x,y)#61

      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;.

   3. 6

      In ordinary differential equations (by analogy with the case for polynomial and…

      In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):

   4. 7

      In abstract algebra and geometry

      In abstract algebra and geometry:

   5. 8

      In miscellaneous other senses

      In miscellaneous other senses:

The neighborhood

• synonymhomogeneous
• synonyminvariable
• synonymof a piece
• synonymonefold
• synonymsamely
• synonymuniform
• synonymuniformal
• synonymunmixed
• synonymunvaried
• synonymunvarying
• antonymheterogeneous
• antonyminhomogeneous
• neighborhomogeneity
• neighborhomogenesis
• neighborhomogenise
• neighborhomogenize
• neighborhomogeny
• neighborconnatural
• neighbormonolithic
• neighbormonotone
• neighborsteady
• neighborunalloyed