Definition:Isotropic Quadratic Form

Definition
Let $\mathbb K$ be a field of characteristic $\operatorname{char}\mathbb K \neq 2$.

Let $V$ be a vector space over $\mathbb K$.

Let $q : V\times V \mapsto \mathbb K$ be a quadratic form.

Then $q$ is isotropic it represents $0$.

That is: $q(v) = 0$ for some $v\in V\setminus\{0\}$.

Anisotropic Quadratic Form
A quadratic form that is not isotropic is said to be anisotropic.

Also see

 * Definition:Nondegenerate Quadratic Form