different between homogeneous vs contravariant

English

Alternative forms

• homogenous (may be considered incorrect; see usage note at homogenous)

Etymology

From Medieval Latin homogeneus, from Ancient Greek ???????? (homogen?s, “of the same race, family or kind”), from ???? (homós, “same”) + ????? (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

Pronunciation

• (UK) IPA^(key): /?h?.m?(?)?d?i?.n??s/, /?h??.m?(?)?d?i?.n??s/
• (US) IPA^(key): /?ho?.mo??d?i?.nj?s/, /?ho?.m??d?i?.nj?s/, /?ho?.mo??d??.nj?s/

Adjective

homogeneous (not comparable)

1. Of the same kind; alike, similar.
2. Having the same composition throughout; of uniform make-up.
   • 1946, Bertrand Russell, History of Western Philosophy, I.25:

     Their citizens were not of homogeneous origin, but were from all parts of Greece.

3. (chemistry) in the same state of matter.
4. (mathematics) Of which the properties of a smaller set apply to the whole; scalable.

   The function ${\displaystyle f(x,y)=x^{2}+y^{2}}$ is homogeneous of degree 2 because ${\displaystyle f(\alpha x,\alpha y)=\alpha ^{2}f(x,y)}$.

Antonyms

• heterogeneous

Derived terms

Related terms

• homogeneity
• homogenise, homogenize

Translations

Further reading

• homogeneous in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• homogeneous in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• homogeneous at OneLook Dictionary Search

English

Adjective

contravariant (not comparable)

1. (category theory, of a functor) which reverses composition
2. (object-oriented programming) Using or relating to contravariance.

Translations

Noun

contravariant (plural contravariants)

1. (algebra) A bihomogeneous polynomial in dual variables of x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

Translations