Authors’ abstract: Which collections of the $mn$ minors of an $m$-by-$n$ matrix uniquely determine the matrix, given some regularity conditions? For $m=n=3$, the 585 such collections, that are distinct up to symmetry, are determined. For general $m, n$, a necessary and a sufficient condition for reconstruction are given in terms of matchings in a bipartite graph. Among other particular results, those collections of entries for which there are minors that permit a reconstruction one entry at a time are characterized.
Reviewer: Kaiming Zhao (Waterloo)