Dimension of Radical of Bilinear Form

Theorem
Let $\mathbb K$ be a field.

Let $V$ be a vector space over $\mathbb K$ of finite dimension $n>0$.

Let $f$ be a bilinear form on $V$.

Let $\operatorname{rad}(V)$ be the radical of $V$.

Let $\operatorname{rk}(f)$ be the rank of $f$.

Then $\dim(\operatorname{rad}(V)) = n - \operatorname{rk}(f)$.