Is there accepted terminology for multisets of vectors that are "as independent as possible"? Let $V$ denote a finite-dimensional real vector space. Suppose $A$ is a multiset of elements of $V$. Then if $\mathrm{card}(A) > \mathrm{dim}(V)$, it follows that $A$ cannot be linearly independent. Nonetheless, it may be the case that these vectors are "as independent as possible," meaning that for every submultiset $B$ of $A$ with $\mathrm{card}(A)=\mathrm{dim}(V),$ it holds that $B$ is linearly independent. For instance, the multiset $$\left\{[1 \;\; 0], [1/2 \;\; 1/2], [0 \;\; 1]\right\}$$ is "as independent as possible," whereas $$\left\{[1 \;\; 1], [1/2 \;\; 1/2], [0 \;\; 1]\right\}$$ is not.

Question. Is there accepted terminology for multisets of vectors that are "as independent as possible"?

 A: The concept you are looking for may be that of general position, where no subset has any more dependence relations than necessary. This means that if $k\leq\dim(V)$, any subset with $k$ elements will span a $k$-dimensional subspace. 
"General position" can also be applied in other situations both within and outside of linear algebra (indeed, the linked Wikipedia article focuses mainly on algebraic geometry) and vaguely means that there are no "coincidences." Sticking with linear algebra for the moment, we can say that a set of $2$-dimensional subspaces is in general position if there are no unnecessary intersections. In $3$-dimensional space two planes can't help but intersect in a line. Any set of two planes in $3$-space is in general position, but a set of three planes is only in general position if they do not all intersect in the same line.
A: When referring to a linear map rather than a set (so, the canonical linear map from a vector space which has $A$ as a basis to $V$), you can say that the map has "full rank".  That is, it has the maximal possible rank that it could have.  I don't know how common it is to use "full rank" to describe a set rather than a map, but it seems natural enough to do so and I think that the meaning would be immediately understood.
