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In algebra linear , un forma sesquilinear [ 1] function
f
:
V
×
W
→
F
:
(
v
,
w
)
↦
f
(
v
,
w
)
=
⟨
v
,
w
⟩
{\displaystyle f:V\times W\rightarrow F:(v,w)\mapsto f(v,w)=\langle v,w\rangle }
spatios vectorial complexe
V
{\displaystyle V}
W
{\displaystyle W}
scalar del corpore
F
{\displaystyle F}
F
=
C
{\displaystyle F=\mathbb {C} }
v
,
v
1
,
v
2
∈
V
{\displaystyle v,v_{1},v_{2}\in V}
w
,
w
1
,
w
2
∈
W
{\displaystyle w,w_{1},w_{2}\in W}
λ
∈
C
{\displaystyle \lambda \in \mathbb {C} }
⟨
v
1
+
v
2
,
w
⟩
=
⟨
v
1
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w
⟩
+
⟨
v
2
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w
⟩
{\displaystyle \langle v_{1}+v_{2},w\rangle =\langle v_{1},w\rangle +\langle v_{2},w\rangle }
⟨
λ
v
,
w
⟩
=
λ
¯
⟨
v
,
w
⟩
{\displaystyle \langle \lambda v,w\rangle ={\overline {\lambda }}\;\langle v,w\rangle \quad \quad \quad \quad \quad \quad \quad \quad }
Semilinearitate in le prime argumento )
⟨
v
,
w
1
+
w
2
⟩
=
⟨
v
,
w
1
⟩
+
⟨
v
,
w
2
⟩
{\displaystyle \langle v,w_{1}+w_{2}\rangle =\langle v,w_{1}\rangle +\langle v,w_{2}\rangle }
⟨
v
,
λ
w
⟩
=
λ
⟨
v
,
w
⟩
{\displaystyle \langle v,\lambda w\rangle =\lambda \,\langle v,w\rangle \quad \quad \quad \quad \quad \quad \quad \quad }
Linearitate in le secunde argumento ).In le corpore
R
{\displaystyle \mathbb {R} }
numeros real , le forma sesquilinear concorda con le forma bilinear.
↑
Derivation (in ordine alphabetic):
(ca ) ||
(de) Sesquilinearform ||
(en) (es) (fr) (it) (pt) (ro )
|| (ru) Полуторалинейная форма
