Générateurs du groupe linéaire

n>2K
Tij (λ) = In+λEij i6=j λ ∈K
Di(α) = In+ (α−1)Eii α∈K∗
n(K)
n(K)
n(K)
Tij (λ)
Li←Li+λLjCj←Cj+λCi
Tij (1)Tji(−1)Tij (1) LiLjLj−Li
A∈n(K)A
A i >2ai16= 0
L1←L1−a11 −1
ai1Li1 (1,1) a11 6= 0
L1←L2L2← −L1
(1,1)
M1, . . . , MpN1, . . . , Nq
Mp. . . M1AN1. . . Nq=1 0
0A1
A1∈n−1(K)
A1
1
1
α
α= det A
U1, . . . , UrV1, . . . , Vr
A=Ur. . . U1Dn(det A)V1. . . Vs
n(K)n(K)
K=n(K)

A∈n(K)A In
X[|1, n|]2\ {(i, i), i ∈[|1, n|]}
(λC)C∈X
A=Y
C∈X
TC(λC)
ϕ: [0,1] −→ n(K)
t7−→ At=Q
C∈X
TC(tλC)ϕ(0) = Inϕ(1) = A
n( )
n( )
M=In+λEij D
M=D−1(DM)
D−1DM
D
n( )