Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm given that a quadratic form $q$ is positive definite if $q(v) > 0 \quad \forall 0 \neq v \in V$ and equivalently for bilinear form $\tau$. Does this mean that in a positive definite bilinear form there can exists $v,w \in V$ such that $\tau (v,w) \leq 0$ ?

share|cite|improve this question

1 Answer 1

up vote 2 down vote accepted


If $V=\mathbb{R},$ $\tau:(x,y)\mapsto xy$ is positive definite but $\tau(1,-1)=-1.$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.