bilinear

English

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 $f(x,y)=xy$ is bilinear, because $f(ax+bu,y)=af(x,y)+bf(u,y)$ and $f(x,ay+bv)=af(x,y)+bf(x,v)$ 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

(mathematics) linear in each of two variables

• Armenian: please add this translation if you can
• Chinese:

  Mandarin: please add this translation if you can

• Czech: bilineární
• Finnish: bilineaarinen
• French: bilinéaire (fr)
• Georgian: please add this translation if you can
• German: bilinear
• Italian: bilineare
• Polish: dwuliniowy
• Russian: билине́йный (ru) (bilinéjnyj)
• Spanish: bilineal

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

Positive forms of bilinear (uncomparable)

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist bilinear	sie ist bilinear	es ist bilinear	sie sind bilinear
strong declension (without article)	nominative	bilinearer	bilineare	bilineares	bilineare
	genitive	bilinearen	bilinearer	bilinearen	bilinearer
	dative	bilinearem	bilinearer	bilinearem	bilinearen
	accusative	bilinearen	bilineare	bilineares	bilineare
weak declension (with definite article)	nominative	der bilineare	die bilineare	das bilineare	die bilinearen
	genitive	des bilinearen	der bilinearen	des bilinearen	der bilinearen
	dative	dem bilinearen	der bilinearen	dem bilinearen	den bilinearen
	accusative	den bilinearen	die bilineare	das bilineare	die bilinearen
mixed declension (with indefinite article)	nominative	ein bilinearer	eine bilineare	ein bilineares	(keine) bilinearen
	genitive	eines bilinearen	einer bilinearen	eines bilinearen	(keiner) bilinearen
	dative	einem bilinearen	einer bilinearen	einem bilinearen	(keinen) bilinearen
	accusative	einen bilinearen	eine bilineare	ein bilineares	(keine) bilinearen

Related terms

• linear
• multilinear

Further reading

• “bilinear” in Duden online