Definition:Degenerate Bilinear Form

Definition
Let $\mathbb K$ be a field.

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

Let $b : V\times V \to \mathbb K$ be a bilinear form on $V$.

Then $b$ is degenerate there exists $v\in V\setminus\{0\}$ such that $b(v,u) = 0$ for all $u\in V$.

Also see

 * Definition:Radical of Bilinear Form