bilinear functional on complex vector space Given a complex vector space S, if g: S $\times$ S $\rightarrow$ $\mathbb{C}$ is a symmetric bilinear functional, can we say there always exist v $\in$ S and w $\in$ S such that g(v,w) = 0?
Yes.  Just take either $v$ or $w$, or even both, to be the zero vector.
Yes.  Just take either $v$ or $w$, or even both, to be the zero vector.