Semaine 13

E F Kf:E→F E0
E f(E0)F
ERE×E
∀(x, y) (x0, y0)∈E×E(x, y) + (x0, y0) = (x+x0, y +y0),
∀(x, y)∈E×E∀z=a+ib ∈C(a+ib).(x, y) = (ax −by, ay +bx).
E×EC
E, F, G Kv:E→F u :F→G u ◦v= 0
Imv ⊂Keru
EK
E f :E→E
Kerf ⊂Kerf2
Kerf =Kerf2Imf ∩Kerf ={0}
F={(x, y, z)∈R3x+y−z= 0}G={(a−b, a +b, a −3b)a, b ∈R}
F G R3
F∩G
E, F f :E→F f Kerf ={0}
E
E=R2F=V ect(e1)G=V ect(e2)e1= (1,0) e2= (0,1) F∪G
F, G E F ∪G E F ⊂G G ⊂F
X E
EaF(X, E)→E
f7→ f(a).
Ea
E F Kf:E→F E0
E f(E0)F
ERE×E
∀(x, y) (x0, y0)∈E×E(x, y) + (x0, y0) = (x+x0, y +y0),
∀(x, y)∈E×E∀z=a+ib ∈C(a+ib).(x, y) = (ax −by, ay +bx).
E×EC
E, F, G Kv:E→F u :F→G u ◦v= 0
Imv ⊂Keru
EK
E f :E→E
Kerf ⊂Kerf2
Kerf =Kerf2Imf ∩Kerf ={0}
F={(x, y, z)∈R3x+y−z= 0}G={(a−b, a +b, a −3b)a, b ∈R}
F G R3
F∩G
E, F f :E→F f Kerf ={0}
E
E=R2F=V ect(e1)G=V ect(e2)e1= (1,0) e2= (0,1) F∪G
F, G E F ∪G E F ⊂G G ⊂F
X E
EaF(X, E)→E
f7→ f(a).
Ea