grandes-ecoles 2010 QII.C.3

grandes-ecoles · France · centrale-maths2__mp Proof Proof of Set Membership, Containment, or Structural Property

For the rest of this problem, we assume that $\varphi$ is a non-degenerate symmetric bilinear form on $E$, and we denote by $q$ its quadratic form.
Show that $\bar{F} = G \oplus P_1 \oplus \ldots \oplus P_s$ is non-singular. We will say that $\bar{F}$ is a non-singular completion of $F$.

For the rest of this problem, we assume that $\varphi$ is a non-degenerate symmetric bilinear form on $E$, and we denote by $q$ its quadratic form.

Show that $\bar{F} = G \oplus P_1 \oplus \ldots \oplus P_s$ is non-singular. We will say that $\bar{F}$ is a non-singular completion of $F$.

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