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TSI2
no3
M2+M=A
A=5 3
1 3 M2(R)
A
A
λ1λ2λ1> λ2
A
D=λ10
0λ2
PM2(R)D=P−1AP
N=x y
z t M2(R)
N2+N=D
ND =DN y =z= 0
t2+t= 2
x2+x= 6
N
N
N2+N=D
MM2(R)N=x y
z t x, y, z, t R
M2(R)N=P−1MP
P−1M x, y, z t
M2+M=A⇐⇒ N2+N=D
MM2(R)
M2+M=A
a
Ma=a−1−1
2a+ 2 
a Ma
a Ma
Ma

P2×2Da=P−1MaP
P−1
a b MaMb=MbMa
n An
An=M1M2M3. . . Mn
n M1, M2, . . . , Mnn
an, bn, cn, dn
An=anbn
cndn.
(un)n>1(vn)n>1u1=−2v1= 4
∀n∈N, un+1 = (n−1)un−vnvn+1 = 2un+ (n+ 2)vn.
n un
E=R3[X]f
E P ∈E f(P)
f(P)(X) = −3XP (X) + X2P0(X), P 0P.
E
f E
M f E
M n ∈N∗Mn
Ker f f Ker f
Im f f
IdE0EE
v E v0= IdEkN∗vk=v◦vk−1
u g E u4= 0Eu36= 0Eg= IdE+u+u2+u3
P E P ∈/Ker(u3)P, u(P), u2(P), u3(P)
E
g E g−1
u
Ker u= Ker(g−IdE)
1g
(E, +, .)Rf E F (E, +, .)
F f ∀−→ x∈F f(−→ x)∈F

TSI2
MM3(R)
M=
3 1 2
1 1 0
−112
I33
M
M
M
MT
λ∈RM MT
MT
MT
(E, +, .)Rf E
{−→ 0}E E f
F E −→ 0p
FBF= (−→ u1,−→ u2,...,−→ up)F
F f ∀k∈[[1, p]] f(−→ uk)∈F
f
F E 1BF= (−→ u)F
F f −→ u f
(E, +, .)R3BE= (−→ e1,−→ e2,−→ e3)f
E A BE
FBE
BF= (−→ u1,−→ u2)F−→
u3EUE= (−→ u1,−→ u2,−→ u3)
E
QUEBE
Q=
a1b1c1
a2b2c2
abc
a, b c
−→
x E
X=
x1
x2
x3
−→
xBE
X0=
x0
1
x0
2
x0
3
−→
xUE
Q, X X0
x0
3=ax1+bx2+cx3

−→
x E (x1, x2, x3)
BE−→
x∈F⇐⇒ ax1+bx2+cx3= 0.
ax1+bx2+cx3= 0 FBE
UE
F f
F f
fUEB
B=
α1β1γ1
α2β2γ2
0 0 γ
α1, β1, γ1, α2, β2, γ2, γ ∈R
QTBT=ATQT
a
b
c
AT
a
b
c
AT
λ
abc×A=λabc
−→
x E
X=
x1
x2
x3
−→
xBE
Y=
y1
y2
y3
f(−→
x)BE
ay1+by2+cy3=λ(ax1+bx2+cx3)F f
(E, +, .)R3BE= (−→ e1,−→ e2,−→ e3)f
E M BE
M=
3 1 2
1 1 0
−1 1 2
E f