Processing math: 100%
Norm
Set
context
F
… subfield of
C
context
V
…
F
-vector space
definiendum
p
∈
N
o
r
m
(
V
)
postulate
p
:
V
→
R
v
,
w
∈
V
postulate
p
(
v
+
w
)
≤
p
(
v
)
+
p
(
w
)
postulate
p
(
v
)
=
0
⟹
v
=
0
λ
∈
F
postulate
p
(
λ
⋅
v
)
=
|
λ
|
⋅
p
(
v
)
Discussion
p
(
v
)
≥
0
The last axiom
p
(
v
)
=
0
⟹
v
=
0
isn't part of
seminorm
.
Reference
Wikipedia:
Norm
Parents
Subset of
Seminorm
Parents of
Metric