  With $k$ an infinite field and $\tau_1,\tau_2$ endomorphisms of $k^m$, we
provide a dimension bound on an open locus of a determinantal scheme, under
which, for a general subspace $V \subseteq k^m$ of dimension $n \le m/2$, for
$v_1,v_2 \in V$ we have $\tau_1(v_1)=\tau_2(v_2)$ only if $v_1=v_2$.
Specializing to permutations composed by coordinate projections, we obtain an
abstract proof of the unlabeled sensing theorem.
