# Completion of Nondegenerate Bases

## Theorem

Let $\struct {V, q}$ be an $n$-dimensional scalar product space.

Let $\tuple {v_1, \ldots, v_k}$ be a nondegenerate $k$-tuple in $V$ with $0 \le k < n$.

Then there exist vectors $v_{k+1}, \ldots, v_n \in V$ such that $\tuple {v_1, \ldots, v_n}$ is a nondegenerate basis for $V$.