grandes-ecoles 2022 Q9

grandes-ecoles · France · centrale-maths1__official Groups Symplectic and Orthogonal Group Properties

Show that the restriction $\omega _ { F }$ of $\omega$ to $F ^ { 2 }$ defines a symplectic form on $F$ if and only if $F \oplus F ^ { \omega } = E$.

Show that the restriction $\omega _ { F }$ of $\omega$ to $F ^ { 2 }$ defines a symplectic form on $F$ if and only if $F \oplus F ^ { \omega } = E$.