Definition:Isotropic Quadratic Form

Definition

Let $\mathbb K$ be a field of characteristic $\Char {\mathbb K} \ne 2$.

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 if and only if it represents $0$.

That is: $\map q v = 0$ for some $ v \in V \setminus \set 0$.

Anisotropic Quadratic Form

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

Also see

• Definition:Nondegenerate Quadratic Form

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