grandes-ecoles 2010 QIV.B.4

grandes-ecoles · France · centrale-maths2__mp Groups Symplectic and Orthogonal Group Properties
We propose to prove Witt's theorem, whose statement is: ``let $F$ and $F'$ be two vector subspaces of $E$ such that there exists an isometry $f$ from $(F, q_{/F})$ to $(F', q_{/F'})$. Then there exists $g \in O(E,q)$ such that $g_{/F} = f$.''
Prove Witt's theorem. 
We propose to prove Witt's theorem, whose statement is: ``let $F$ and $F'$ be two vector subspaces of $E$ such that there exists an isometry $f$ from $(F, q_{/F})$ to $(F', q_{/F'})$. Then there exists $g \in O(E,q)$ such that $g_{/F} = f$.''

Prove Witt's theorem.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QI.B.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QIII.A.1 QIII.A.2 QIII.B.1 QIII.B.2 QIII.B.3 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4