126 : endomorphismes diagonalisables en dimension

u∈ L(E)
M∈Mn(K)
u∈ L(E)
K⊂L
K−ev L −ev
A=1/2√3/2
−√3/2 1/2
Pi
Ker(QPi(u))
Ker(Pi(u))
A=
0 2 −1
3−2 0
−2 2 1

λi
Eipi
pipj=δij u=Pλipipi
iPpi=Id
pipj= 0 Ppi=Id λiu=λipi
λipi
P−1AP P −1BP
ui
Ai
F
E⇒uF
u Im(u)
M=
0001
0 0 −1 0
0100
−1 0 0 0
f2= 0
∆=2tr(u2)−tr(u)2
∆6= 0 tr(u2)6=tr(u)2
∆=0 tr(u2)6=tr(u)2(2tr(u))−1

K q uq=u
λ Ker(f−λId)Im(f−λId)
u−λId
K exp(M)
ulu
Kerul=Keru
R
C
Gln(k)
Gln(K)GLm(K)n=m

C
λ v0wk+1 =Avk
vk+ 1 = wk+1/||wk+1 || vkλ
wkλ