D:f7→ f0V
fR C
a, b
∀z∈C, f(z) = az +bz
a b f
A∈ Mn(C)ϕA∈ L(Mn(C))
ϕA(M) = AM
ϕA
A= (ai,j )∈ Mn(R)
∀i∈ {1, . . . , n},|ai,i|>X
j6=i
|ai,j |
A
∀i∈ {1, . . . , n}, ai,i >0
det A > 0
A= (ai,j )∈ Mn(C)A= (ai,j )∈ Mn(C)
det(A) det A
A∈ Mn(C)tA=Adet A∈R
A2n+ 1
det A= 0
A
det(ai,j ) det((−1)i+jai,j ) (ai,j )1≤i,j≤n∈ Mn(K)
A∈ Mn(R)
∀i, j ∈ {1, . . . , n}, ai,j ∈ {1,−1}
2n−1|det A
A∈ Mn(K)C1, . . . , Cn
B
C1−C2, . . . , Cn−1−Cn, Cn−C1
A∈ Mn(R) GLn(Z)A
A∈GLn(Z)|det A|= 1
A, B ∈ Mn(R)
∀k∈ {0,1,...,2n}, A +kB ∈GLn(Z)
det Adet B
A∈ Mn(R)n≥2A1, . . . , AnB∈ Mn(R)
B1, . . . , Bn
Bj=X
i6=j
Ai
det Bdet A