chap3

R C
+
.E,+, .
x, y ∈Ex+y∈E
x, y ∈Ex+y=y+x
x∈Ex+ 0E=x
x∈E−x∈E
x, y, z ∈E(x+y) + z=x+ (y+z)
λ∈Kx∈Eλx ∈E
λ.(µ.x) = (λµ).x ∀λ, µ ∈ ∀x∈

(λ+µ).x =λ.x +µ.x ∀λ, µ ∈ ∀x∈
λ.(x+y) = λ.x +λ.y ∀λ∈ ∀x, y ∈
1.x =x∀x∈
C R
R C
R[X]R
(a0+a1X+... +anXn)+(b0+b1X+... +bnXn) =
(a0+b0)+(a1+b1)X+... + (an+bn)Xn
λ(a0+a1X+... +anXn) = λa0+λa1X+... +λanXn

S={f:→ } S
f, g ∈ S λ∈
f+g:→λf :→
a7→ f(a) + g(a)a7→ λf(a)
1 2
1×2
(x1, y1) + (x2, y2)=(x1+x2, y1+y2)λ(x1, y1)=(λx1, λy1)
λ∈
1×... ×n
1n

Exemplesd’EspacesVectorielset
Notations