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F R4
F={(x;y;z;t)∈R4=x+y=z+t= 0}
a= (2; −2; −1; 1)
a, b, c ∈Rx7→ sin(x+a)
x7→ sin(x+b)x7→ sin(x+c)RR
R4
a= (1; 2; 2; 1), b = (5; 6; 6; 5), c = (−1; −3; 4; 0), d = (0; 4; −3; −1)
a= (2; −5; 3; 10), b = (1; −1; 1; 3), c = (3; 3; 1; 1)
a= (1; 2; 5; −1), b = (3; 6; 5; −6), c = (2; 4; 0; −2)
R4F=V ect(u;v;w)G=V ect(a;b)
u= (1; −1; 2; 3) v= (1; 1; 2; 0) w= (3; −1; 6; −6) a= (0; 2; 0; ..3)
b= (1; 0; 1; 0) F G F ∩G F +G
R4F a = (1,2,3,4)
b= (2,2,2,−2) c= (0,2,4,4) G d = (1,0,−1,2)
e= (2,3,0,1)
F, G, F +G F ∩G
E u ∈ L(E)u
∀x∈E, ∃λx∈K, u(x) = λx.x
f g E
g◦f=IdE
f g E
E
E{0}
dim(E)=1 E E {0}
E, F G f g
E F F G
dim(Ker(g◦f)) ≤dim(Ker(f)) + dim(Ker(g))
f Ker(g◦f)
E u
E
Im(u) = Ker(u)
u2= 0
∃p∈N, dim(E)=2p
rang(u) = p
fR
E=Im(f) + Ker(f)⇔Im(f) = Im(f2)
EKn u, v ∈ L(E)
v◦u= 0 u+v rang(u) + rang(v) = n