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

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

Then:
 * $\dim \left({\operatorname{rad} \left({V}\right)}\right) = n - \operatorname{rk} \left({f}\right)$

where $\dim$ denotes dimension.