Uniqueness conditions for low-rank matrix recovery (Q442534)

The authors address the problem of recovering an unknown low-rank matrix from few linear measurements. In this respect, they consider the theoretical question of how many measurements are needed via any method whatsoever -- tractable or not, and show thet for a family of random measurements ensembles \(m \geqslant 4nr - 4r^2\) and \(m \geqslant 2nr - r^2 + 1\) measurements are sufficient to guarantee strong recovery and weak recovery, respectively, by rank minimization (where \(n\) is the dimension of the matrix and \(r\) the fixed rank value).