# bilinear

## English

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### Etymology

From bi- +‎ linear.

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. () Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
bilinear isotropic hardening

### Noun

bilinear (plural bilinears)

1. (linear algebra) A bilinear function.