f:VxV -> F

we call f a withered form if there's a vector $\displaystyle v\ne 0$ for whichf(v,u)=0 for all u in V.

Could f be not-withered, while there still is a $\displaystyle v\ne 0$ for whichf(u,v)=0 for all u in V?

(BTW :$\displaystyle f(u,v)=[u]^t_{B}[f]_B[v]_B$ for any base B of V)