If $V$ over $\mathbb{C}$, $\dim V\ge 2$, let $q: V \rightarrow \Bbb{C}$ be a Quadratic form. s.t. exists $v \ne 0$ such that $q(v)=0$
Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?