Examen Blanc Algèbre III - ENSA Marrakech

E. a ∈E ϕ
E ϕ 6= 0. f :E−→ E
∀x∈E, f(x) = x+ϕ(x)a
f
f
∀x∈E, ϕ(x) = −2(a|x)
f
f
E=Mn(R)hA|Bi=tr(tAB)P∈ On(R)
f:E−→ E
A7→ AP
f
f E
a E
g:E−→ E
f(x) = hx|aia+a∧x.
g E
g∈O(E).
g(a, u, v)
g∈SO(E)
E
e= (e1, e2, e3). u E
M=1
9
744
4 1 −8
−4 8 −1
u E;
QR M