1. Résumé 2. Introduction 3. Definition

E
F
E
F
a
f(a)=1,5a
a
a b
g(a, b)=1,5a+ 1,2b g
E=2F=
f
E F f E
F f x y
E λ µ
f(λx +µy) = λf(x) + µf(y)
(e1, . . . , en)E f
f(e1), . . . , f(en)
x E x =λ1e1+
· · · +λnen
f(x) = f(λ1e1+· · · +λnen) = λ1f(e1) + · · · +λnf(en)

f E F
•f f E
f
•f f
E
E
F
E
H f E f1fp
f x1f1x1
x1=k1+h1H
h2hph1hp
λ1h1+... +λphp= 0 f(λ1h1+... +λphp) = 0 = λ1y1+... +λpyp
y1, ...yph1hp
h H f(h)Im(f)
y1, ...ypf(h) = λ1y1+... +λpyp=
f(λ1h1+... +λphp)
f(h−λ1h1−... −λphp) = 0.
h−λ1h1−... −λphpH
h h1, ..., hp
H H p
E H
H

g
E i j
E
•i j E
•f E E f(i) = i
f(j)=0 f
•f E E f(i) = j
f(j) = i f
•E
F={f;f(x) = acos(x)+bsin(x)a, b ∈
}
• F
•fFf0F
•D f f0
D D
n={(x1, x2, . . . , xn); xi∈ }
•f f((x1, x2, x3, x4)) = (x1, x1, x2, x2)
4 4
•
3
P={(x1, x2, x3)∈3x1+x2−2x3= 0}.
•P
•P P
•f3
f((x1, x2, x3)) = x1+x2−2x3.
P f P
3
D={(x1, x2, x3)∈3x1+x2−x3= 0 x1=x2}.
•D
•D D
•f3 2
f((x1, x2, x3)) = (x1+x2−x3, x1−x2).
D f D