Espaces vectoriels de dimension finie

F⊂E k
BEBF
FEFF
F E
QnRn
RnQ R
R4(x, y, z, t)
x+ 3y+ 4z= 0
2x+ 2y+z= 0
4y+ 7z= 0
Ei
i6=j Ei∩Ej= 0
(Pi)i∈N
ideg Pi=i{Pi}k[X]
a1, . . . , an
x7→ |x−ai|
x1, . . . , xp∈kn
Vect {x1, . . . , xp}kn
E1E2E
dim (E1+E2) = dim E1+ dim E2−dim (E1∩E2).
E k F G
E F G
E k
E
E n F, G, H
dim F+ dim G+ dim H>2n+ 1 F∩G∩H6={0}
a1, . . . , ak
1
X−a1
,1
(X−a1)2,..., 1 (X−a1)n,1 X−a2
,..., 1
(X−a2)n,..., 1 X−ak
,..., 1
(X−ak)n
C(X)

C(X)
x0=−∞, xn+1 = +∞x1<··· < xn
C1R]xi;xi+1[
Sk>1αk−1, . . . , α0
L:= {u∈ S,∀n∈N, un+k=αk−1un+k−1+··· +α0un}.
L
P Xk−αk−1Xk−1−···−α0
θ∈CL
n > 0θ1, . . . , θn
θ1, . . . , θnS
PL
k⊂k0E k0
E k0k0k E
kdimkE= dimkk0×dimk0E
E k k0
E6={0}k0k
R C
k p n
|k|=pn
k⊂k0p
n m n m |k|=pn|k0|=pm
x P
P∈Q[X]P(x)=0 x
√2√3√2 + √3
xQ[x] := {R(x), R ∈Q[X]}R Q
xQ
xQ[x]
x P x
P
xQ[x]
1
√2+√3√2 + √3
x y Q[x, y] := {R(x, y), R ∈Q[X, Y ]}
Q
P6= 0 P(x)=0 Q6= 0
Q(y) = 0 R6= 0 R(x+y)=0

Q:= {z∈C, z }Q