x, y ∈E
(x|y) = 1
4kx+yk2− kx−yk2=1
2kx+yk2− kxk2− kyk2
E E ×E d
∀(x, y)∈E×E, d(x, y) = kx−yk
d
d E
(D0)d E ×ER+
(D1)∀x, y ∈E, d(x, y) = 0 ⇐⇒ x=y
(D2)∀x, y ∈E, d(x, y) = d(y, x)
(D3)∀x, y, z ∈E, d(x, z)6d(x, y) + d(y, z)
x, y ∈E
x y ⇐⇒ (x|y)=0
A, B E
A B ⇐⇒ ∀x∈A, ∀y∈B, (x|y) = 0
A E A
A⊥=y∈E / ∀x∈A, (x|y) = 0
A⊥E
A⊂B B⊥⊂A⊥
A⊥= (Vect A)⊥