Lineare Algebra 2/Gemischte Satzabfrage/15/Aufgabe/Lösung
Jede eigentliche, lineare Isometrie
φ
:
R
2
⟶
R
2
{\displaystyle \varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{2}}
Es sei
P
{\displaystyle {}P}
E
{\displaystyle {}E}
K
{\displaystyle {}K}
r
>
0
{\displaystyle {}r>0}
P
{\displaystyle {}P}
G
{\displaystyle {}G}
P
{\displaystyle {}P}
A
{\displaystyle {}A}
B
{\displaystyle {}B}
C
∈
K
{\displaystyle {}C\in K}
A
,
B
,
C
{\displaystyle {}A,B,C}
C
{\displaystyle {}C}
Es sei
K
{\displaystyle {}K}
V
1
,
…
,
V
n
{\displaystyle {}V_{1},\ldots ,V_{n}}
K
{\displaystyle {}K}
V
1
∗
⊗
⋯
⊗
V
n
∗
⟶
(
V
1
⊗
⋯
⊗
V
n
)
∗
,
f
1
⊗
⋯
⊗
f
n
⟼
(
v
1
⊗
⋯
⊗
v
n
↦
f
1
(
v
1
)
⋯
f
n
(
v
n
)
)
.
{\displaystyle V_{1}^{*}\otimes _{}\cdots \otimes _{}V_{n}^{*}\longrightarrow {\left(V_{1}\otimes _{}\cdots \otimes _{}V_{n}\right)}^{*},\,f_{1}\otimes _{}\cdots \otimes _{}f_{n}\longmapsto {\left(v_{1}\otimes _{}\cdots \otimes _{}v_{n}\mapsto f_{1}(v_{1})\cdots f_{n}(v_{n})\right)}.}
