bilinear

English

Etymology

From bi- +‎ linear.

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
• bilinearization
• bilinearly

Related terms

• multilinear

Translations

(mathematics) linear in each of two variables

• Czech: bilineární
• Finnish: bilineaarinen
• French: bilinéaire (fr)
• (deprecated template usage) {{trans-mid}}
• German: bilinear
• Italian: bilineare
• Polish: dwuliniowy

Noun

bilinear (plural bilinears)

1. (linear algebra) A bilinear function.

Anagrams

• Liberian

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German

Adjective

bilinear (not comparable)

1. bilinear

Related terms

• linear
• multilinear

Further reading

• “bilinear” in Duden online