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by
Ciro Santilli
(
@cirosantilli,
37
)
Norm induced by the complex dot product
...
Area of mathematics
Calculus
Topology
Real coordinate space
Complex coordinate space
Complex dot product
Updated
2025-07-16
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Norm induced by an inner product
Given:
x
=
∑
k
=
1
n
a
k
+
b
k
i
∈
C
n
,
a
k
,
b
k
∈
R
(1)
the norm ends up being:
∣
x
∣
=
∑
k
=
1
n
a
k
2
+
b
k
2
(2)
E.
g
. in
C
2
:
∣
(
2
+
3
i
,
−
1
+
5
i
)
∣
=
2
2
+
3
2
+
(
−
1
)
2
+
5
2
=
4
+
9
+
1
+
25
=
39
(3)
Ancestors
(8)
Complex dot product
Complex coordinate space
Real coordinate space
Topology
Calculus
Area of mathematics
Mathematics
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