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E u1, ..., unx1, ..., xpE
u1, ..., unx1, ..., xp
u1, ..., un
x1, ..., xp
K K =RouC)K
{0}K
(F(R,R),+, .)
R
F={(x, y, z)∈K3,5x2+y2+z2+ 2xy −2yz −2xz = 0}K=R K =C)
K
E A B E
1) vect(A∪B)vect(A)∪vect(B) 2) vect(A∩B)vect(A)∩vect(B)
3) vect(vect(A)) vect(A)
F G E
F∪G E F ⊂G
G⊂F
E=R3F={(x, y, z)∈E, x +y+z= 0}
G={(x, x, x), x ∈R}
F G E
E E
R
F1F2
E
E f E
f2−3f+ 2IdE= 0
f Ker(f−IdE)Ker(f−2IdE)
E f, g ∈ L(E)
f(Ker g ◦f) = Ker g ∩Im f
EKg E
CgL(E)L(E)∀f∈ L(E), Cg(f) = f◦g−g◦f
CgL(E)
gCg
E p q E
α0 1 p◦q=αq ◦p
p◦q=q◦p= 0 p q
p q p +q
p+q
ER
Ψ : E→E
f7→ f00 −3f0+ 2f
Ψ
EKu v L(E)
u◦v−v◦u=u n ∈N, un◦v−v◦unu n