Definition talk:Nondegenerate Tuple of Elements of Scalar Product Space

Comment to User:Usagiop
The formulation could be clearer. I would write the requirement as:


 * Suppose for each $j \in \set {1, \ldots, k}$ and for all $i_1, \ldots, i_j \in \set {1, \ldots, k}$ with $i_1 < i_2 < \ldots < i_j$ that:
 * the vectors $\tuple {v_{i_1}, \ldots, v_{i_j} }$ span a nondegenerate $j$-dimensional subspace of $V$.

However, I do not have access to the cited source, so I cannot be certain what the actual definition is. --Anghel (talk) 14:44, 27 January 2023 (UTC)


 * Thank you for pointing out my mistake. You are right. I improved my comment, since this definition seems still wrong. I guess the original definitions should require any $j$-subtuple of the given $k$-tuple to span a $j$-dimensional degenerate space. Someone should check it. --Usagiop (talk) 15:11, 27 January 2023 (UTC)


 * Sorry you have already written the same. --Usagiop (talk) 15:18, 27 January 2023 (UTC)


 * Now I think again it should be that $\tuple {v_1,\ldots,v_j}$ for all $1\le j \le n$ spans a $j$-dim degenerate space. I am waiting for more input here. --Usagiop (talk) 15:30, 27 January 2023 (UTC)