Algèbre linéaire / Intégrales multiples - Jean

E F
f g E F
rg(f)−rg(g) ≤rg(f+g)≤rg(f) + rg(g)
f, g ∈ L(E)fg = 0 f+g
rg(f) + rg(g) = E
RRDxy dxdy D =(x, y)∈R2,0≤x, 0≤y, x +y≤1
E p, q ∈ L(E)
p+q p ◦q=q◦p= 0
p+q(p+q) = p⊕q(p+q) = p∩q
RRDx2dxdy D =(x, y)∈R2, x2≤y≤x
E f ∈ L(E)
E=f⊕f⇐⇒ f=f2
RRD(x2−y2)exy dxdy D =(x, y)∈R2, x2+y2≤1, x +y≥1, x ≥y
f g E
E=f g =f+g
RRDxcos(px2+y2) dxdy D =(x, y)∈R2,0≤y≤x, x2+y2≤π2

E F
E=F
Sn(R)n
An(R)n
Mn(R)
RRD
1
x+y+1 dxdy D =(x, y)∈R2,0≤x≤1, x2≤y≤x
EK K =R K =Cϕ1, ..., ϕp∈E∗ϕ:E−→ Kp
ϕ= (ϕ1, ..., ϕp)ϕ ϕ1, ..., ϕp
RRD
x2
a2+y2 b2dxdy D =(x, y)∈R2, x2+y2≤R2
(a, b, R)∈(R∗
+)3
Mn(K)K=R K =C
RRDe−(x2+xy+y2)dxdy D =(x, y)∈R2, x2+xy +y2≤1
ERn≥2
1≤p≤n p e∗
1, e∗ 2, ..., e∗ pH1, H2, ..., Hp
∪p
k=1Hk6=E
RRD
1
1+x2+y2dxdy D =(x, y)∈R2, x2+y2≤1