1.AdjectiveLinear (preserving linear combinations) in each variable."The function
f
(
x
,
y
)
=
x
y
{\displaystyle f(x,y)=xy}
is bilinear, because
f
(
a
x
+
b
u
,
y
)
=
a
f
(
x
,
y
)
+
b
f
(
u
,
y
)
{\displaystyle f(ax+bu,y)=af(x,y)+bf(u,y)}
and
f
(
x
,
a
y
+
b
v
)
=
a
f
(
x
,
y
)
+
b
f
(
x
,
v
)
{\displaystyle f(x,ay+bv)=af(x,y)+bf(x,v)}
for all values."