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 $V$.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Pseudo-Riemannian Metrics