Definition:Nondegenerate Tuple of Elements of Scalar Product Space

Definition

Let $\struct {V, q}$ be the scalar product space.

Let $v_i \in V$ for $i \in \N_{> 0}$.

Let $\tuple {v_1, \ldots, v_k}$ an ordered $k$-tuple.

Suppose, for each $j \in \N_{> 0}$ such that $j \le k$ vectors $\tuple {v_1, \ldots, v_j}$ span a nondegenerate $j$-dimensional subspace of $V$.

Then $\tuple {v_1, \ldots, v_k}$ is said to be nondegenerate.

Sources

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