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 if and only if there exists $v \in V\setminus \set 0$ such that $\map b {v, u} = 0$ for all $u \in V$.

Nondegenerate Bilinear Form

A bilinear form on $V$ which is not degenerate is nondegenerate.

Also see

• Definition:Radical of Bilinear Form

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