Linear map
For vector spaces
V
and
W
over field
K
,
f
:
V
→
W
is a linear map if
∀
u
,
v
∈
V
, ∀
c
∈
K
holds:
Additivity:
f
(
u
+
v
) =
f
(
u
) +
f
(
v
)
Homogeneity:
f
(
c
u
) =
c
f
(
u
)