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EK=R C
x, y, a, u
~x, ~y, ~a, ~u α, β, λ, µ
A E ~x ∈E
~x A (−→ a1,−→ a2,...,−→ ak)
A k α1, α2, . . . , αk
~x =α1−→ a1+α2−→ a2+· · · +αk−→ ak
E=M3(K), M =
1 0 0
1 1 0
α1 1
, I3=
100
010
001
M2I3M
M3I3, M M2
(M−I3)3
M0∈ M3(K)M
MM0=M0M=I3
M M0=M−1
Vect A A
Vect ∅=−→ 0E
Vect A E A
Vect A E Vect A A
AVect A
Vect A E
Vect A−→ 0E∈Vect A−→ x A −→ 0E
0−→ x A
Vect A A
AVect A
−→
x∈Vect A λ ∈Kλ−→ x A Vect A
Vect A A −→ x∈A−→ x= 1−→ x∈Vect A

F A Vect A−→ xVect A
−→
x=
n
X
i=1
αi−→ aiαiK−→ aiA A ⊂F−→ ai
F−→ x=
n
X
i=1
αi−→ aiF F
E
Vect A⊂F
F E A F F = Vect A
A F A F
(−→ ai)i∈I
(−→ x1,−→ x2,...,−→ xn)
∀α1, α2, . . . , αn∈K,α1−→ x1+α2−→ x2+· · · +αn−→ xn=−→ 0E=⇒α1=α2=· · · =αn= 0
(−→ x1,−→ x2,...,−→ xn)α1, α2, . . . , αn∈
Kα1−→ x1+α2−→ x2+· · · +αn−→ xn=−→ 0E
P1, P2, . . . , Pn∈K[X]\ {0}deg P1<deg P2<· · · <deg Pn
(P1, P2, . . . , Pn)
(−→ xi)i∈I
I⊂N(Pi)i∈I

E=RR(fa)a∈Rfa:x7→ eax
(fa)a∈Rfa:x7→ |x−a|
R R
(−→ x1,−→ x2,...,−→ xn) (−→ x1,−→ x2,...,−−−→ xn−1)−→ xn
−→
x1,−→ x2,...,−−−→ xn−1
(−→ x1,−→ x2,...,−→ xn)α1, α2,...,αn∈K
α1−→ x1+α2−→ x2+···+αn−→ xn=−→ 0E
αn
α1−→ x1+α2−→ x2+···+αn−1−−−→ xn−1=−→ 0E
α1, α2,...,αn−1
(−→ x1,−→ x2,...,−−−→ xn−1)αn6= 0
−→
xn−→ x1,−→ x2,...,−−−→ xn−1
−→
xn=
n−1
X
i=1 −αi
αn−→
xi
−→
x−→ y−→ x6=−→ 0
λ∈K−→ y=λ−→ x
EKE= (−→ ei)i∈IE
EE⇐⇒ E
EKE= (−→ ei)i∈IE
EE⇐⇒ 
−→
x E
E
−→
xE
E E
−→
x

E
E E
E
dim{−→ 0}= 0
E
EKnE n
E n E Kn
E= (−→ e1,−→ e2,...,−→ en)E−→ x E
−→
x=
n
X
i=1
xi−→ eiϕ:−→ x7→ 
x1
x2
xn
EKnϕ
ϕ
ϕ(−→ x) = 
x1
x2
xn
ϕ(−→ y) = 
y1
y2
yn
ϕ(λ−→ x+−→ y) = λ
x1
x2
xn
+
y1
y2
yn
ϕ
−→
x:
x1
x2
xn
−→
x
E=KnEKn
dim E=n n n
n n

dim E=n F E 6ndim F=n
F=E
F1F2
E
F1⊂F2
dim F1= dim F2=⇒F1=F2
EKn>1f E p
fp= 0
x∈Ex, f(x), f2(x), . . . , fp−1(x)
fn= 0
Kn
1
0
0
0
,
0
1
0
0
,
0
0
1
0
,...,
0
0
0
1
Mpq(K)p q K
Eij i
jMpq(K)p×q
K[X] (Xk)k∈N
Kn[X]K[X]
6n(Xk)06k6n
(Pk)k∈Ndeg Pk=kK[X]
P∈K[X]n= deg P(P0, P2, . . . , Pn)
Kn[X]Kn[X]n+ 1
n+ 1 P
(Pk)k∈NP(Pk)k∈N
A n In, A, A2, . . . , An2
A