Hi everyone, first of all i must admit i'm very familiar with quadratic forms and positive subspaces, so i'm sorry if my question is too trivial. So, here's my problem:


Let $L$ be a real vector space of dimension 22 with quadratic form of signature $(3,19)$. Let $V\subset L$ be a positive space of dimension 2. The space $V^\perp$ should be spanned by positive vectors (i.e. vectors $v\in L$ such that $q(v)>0$) , but how to prove it?


Actually i have no clue at all: $V^\perp$ is a quadratic space with signature $(1,19)$, but i really can't see how it can be generated by positive vectors of $V$.


Thank you



Subspace generated by positive vectors
Any space with at least one positive vector $w$ is spanned by positive vectors: if $v$ is any vector then $v-\lambda w$ is positive for sufficiently large $\lambda$, and so $v=(v-\lambda w)+\lambda w$ is the sum of two positive vectors.


