Let's say I have a set of vectors $V$ in some $d$ dimensional space. Is there a method to combine any subset of vectors in $V$ into a new single vector $v$ such that no other combination of vectors will represent $v$? So, given some unknown combination method $m$, taking a set of vectors and outputs a new vector, $m(a) \neq m(b)$ must hold for all subsets $a,b \in S$ (except when $a = b$).
Thanks!