bilinear

English

English Wikipedia has an article on:

bilinear

Wikipedia

Etymology

From bi- +‎ linear.

Pronunciation

• (UK) IPA^(key): /baɪˈlɪn.i.ə/
• (US, Canada) IPA^(key): /baɪˈlɪn.i.ɚ/
• (General Australian) IPA^(key): /bɑɪˈlɪn.i.ə/

Adjective

bilinear (not comparable)

1. (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.

   The function ${\displaystyle f(x,y)=xy}$ is bilinear, because ${\displaystyle f(ax+bu,y)=af(x,y)+bf(u,y)}$ and ${\displaystyle f(x,ay+bv)=af(x,y)+bf(x,v)}$ for all values.

2. (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).

   bilinear isotropic hardening

Derived terms

• bilinear form
• bilinear transformation
• bilinearity
• bilinearization
• bilinearly

Related terms

• multilinear

Translations

Noun

bilinear (plural bilinears)

1. (linear algebra) A bilinear function.

Anagrams

• Liberian

German

Etymology

From bi- +‎ linear.

Pronunciation

• IPA^(key): /bilineˈaːɐ̯/

Adjective

bilinear (strong nominative masculine singular bilinearer, not comparable)

1. bilinear

Declension

Related terms

• linear
• multilinear

Further reading

• “bilinear” in Duden online